AEM Solid Mechanics Research Seminar

Abstract: The complex mechanical behavior of arteries has long been studied for by combination of axial stretch and pressurization. Notably, when the ends of the vessel are capped during the test, the force on the end caps can rise, fall, or stay flat with increasing pressure depending on the amount of imposed stretch. Some 40 years ago, the observation was made that the axial stretch at which the force vs. pressure (FP) curve is flat is very close to the in vivo stretch of the vessel. Although teleological arguments have been put forward, no mechanism has been proposed for the artery to sense the end force. We have recently found that such sensing may not be necessary because the remodeling of individual fibers within a computationally modeled artery leads to the observed effect with no macroscopic feedback. Rather, the combination of tissue architecture and microscopic remodeling rules results in a vessel whose macroscopic FP curve is flattest at an axial stretch roughly equal to the in vivo stretch. Our results suggest that it is not that the in vivo stretch is the one at which the FP curve is flat, but that for a given in vivo stretch, the artery remodels itself so that the FP curve is flat, based solely on local, microscale remodeling rules. The seminar will discuss the problem, our model, our results, and the further questions that they raise.

Abstract: Today, Bayesian “anything” (inference, statistics, algorithm, learning, etc) is seen as a modern, advanced, state-of-the-art term in the engineering sciences. Why, exactly, is that for such an old theory (from the 1700s)? The ubiquitous Bayes’ theorem was formulated as the answer to a very basic question of chance. It was only later that Laplace grounded it in the rigorous mathematical framework that we know today by surveying France’s population ratio of males to females. Numerous fundamental advances in math together with major algorithmic developments have substantially expanded its applicability to increasingly complex engineering problems. In this talk, I will take you through the history of Bayes’ theorem while introducing its basic technical aspects. We will discuss a practical problem of interest where the reasoning behind the theory is clearly illustrated. Lastly, I will highlight some of the advancements in hypersonics research enabled by the application and further development of this versatile theory. This journey through Bayes’ theorem history and advancements underscores its transformation into a vital tool for scientific research.

Abstract: Continuum finite element (FE) modeling of damage and failure of quasibrittle structures suffers from the spurious mesh sensitivity due to strain localization. This issue has been investigated extensively for deterministic analysis through the development of localization limiters. This talk will present a mechanism-based model to mitigate the mesh sensitivity in stochastic FE simulations of quasibrittle fracture. The present model is formulated within the framework of continuum damage mechanics, and the spatial randomness of material properties is represented by homogenous random fields. Two localization parameters are introduced to describe the evolution of the damage pattern of finite elements. These parameters are used to guide the energy regularization of the constitutive law, as well as to determine the mapping of the random fields of material properties onto the finite element mesh. The model is applied to simulate the stochastic failure of quasibrittle structures of different geometries featuring different behaviors including both distributed and localized damage. It is shown that the existing local projection and local averaging mapping methods could lead to strong mesh dependence of the predicted mean and variance of the structural load capacity. To mitigate the spurious mesh sensitivity, the mapping of the random fields of material properties must be tied to the damage pattern, which may evolve during the loading process. This result has important implications for the recent trends in the machine-learning approach for constitutive modeling of quasibrittle materials.

Abstract: Nitinol is widely used in medical devices including life sustaining permanent implants such as replacement heart valves. The mostly reversible stress-induced phase transition allows near complete recovery from small diameter delivery systems to functional devices with much larger diameters. However, like most any solid, Nitinol is subject to fatigue due to cyclic loads. In this lecture, I show many factors governing Nitinol fatigue by examining the physical and mechanical history of the material from the melt to the in vivo use. Combining this examination with a battery of tests - including testing the Nitinol to failure out to 1 billion cycles and examining the metallography and fractography [1] – analysis shows there are two failure modes – low-cycle fatigue due to phase transitions interacting with inclusions from the melt and ultra-high cycle fatigue due to sub-Kth crack progression from inclusions from the melt. Recent experiments are showing that 100 Million and 1 Billion fatigue life with cyclic phase transformation is possible when inclusions are <2 microns.

[1] Weaver JD, Sena GM, Aycock KI, Roiko A, Falk WM, Sivan S, Berg BT. Rotary Bend Fatigue of Nitinol to One Billion Cycles. Shap Mem Superelasticity. 2023 Jan 18;9:50-73. Rotary Bend Fatigue of Nitinol to One Billion Cycles - PMC (nih.gov)

Abstract: Modern societies have experienced urbanization at an unprecedented rate, which has increased the dependency of the public on the uninterrupted operation of our infrastructure. Therefore, protecting and enhancing the resilience of the built infrastructure under natural hazards is most relevant today. As such, the engineering community must shift towards incorporating more resilient structural systems in the design process, which aim to eliminate or minimize damage, loss of functionality, and downtime in the infrastructure after major natural hazards. As an example of this approach, this presentation provides an overview of the design and experimental validation of Eccentrically Braced Frames (EBFs) equipped with novel cast steel replaceable modular yielding links. The proposed cast steel links primarily aim to enhance the resilience of EBFs under earthquakes and eliminate undesirable failure modes, which are observed in EBFs with conventional and replaceable wide-flange links. In addition, cast steel links promote modular construction and simplify the design process of EBFs. The performance of the proposed yielding links is validated through thirteen large-scale quasi-static tests and twelve pseudo-dynamic hybrid simulations. The results of the experimental program demonstrated highly enhanced ductility and ultra-low-cycle fatigue life for the proposed links, achieving up to 0.21 radians of link rotation under the AISC loading protocol, while all other structural elements remained undamaged. Pseudo-dynamic hybrid simulations are incorporated to develop and validate a low-cost re-centering mechanism in EBFs to reduce their residual deformations and downtime after severe random loading histories such as earthquakes. In the end, design provisions are developed for EBFs designed with cast steel replaceable modular yielding links.

Abstract: Numerous studies in the 1950s-1970s based on linear stability analysis of the single domain state on the shoulder of the hysteresis loop show that this method fails to predict the width of the loop, a conclusion referred to as the ``coercivity paradox’'. We argue that the basic idea of using micromagnetics to predict coercivity is reasonable, but the fault lies with linear stability analysis; one needs to account for large but localized disturbances arising from potent defects. To investigate the prediction of coercivity in this context, we develop an implementation of micromagnetics using the magnetization and vector potential as basic unknowns using the recent work of Di Fratta et al. (SIAM J. Math. Anal. 52, (2020), 10.1137/19M12613652020), and we borrow ideas from the strategy of Balakrishna et al. (npj Computational Materials 8, (2022), 10.1038/s41524-021-00682-7). We have developed a strategy with minimal assumptions, for a soft magnetic material like FeNi, to predict the coercivity and the evolution of magnetic domain patterns under the varying applied field at nano and macro scales. The value of coercivity is controlled by various material parameters like anisotropy constant or exchange constant and so forth. Introducing at the nanoscale largely localized disturbances through defects, a nucleation barrier for the reversal of the magnetization is provided. We have demonstrated that the change in the size of localized disturbance affects the coercivity because the exchange is dominant at the nanoscale. We have also shown that the introduction of magnetostriction(magneto-elastic energy) affects the nucleation barrier, which forces the magnetization to take an alternative path consistent with strain compatibility that in turn increases the coercivity of the material. These alternative paths are seen with completely different magnetic domain patterns formed as local minimizers with the changing applied field. We find that small values of magnetostriction have an important effect on coercivity. The predictions are in a form that can be used for alloy development of soft magnetic materials.

Abstract: Over the last several years, generative artificial intelligence (AI) has been at the heart of the most innovative large language and computer vision developments, e.g., ChatGPT, DALL-E, and Midjourney. Recently, these same techniques have been applied to the chemical and material sciences. In this talk, I will survey recent work performed by the likes of DeepMind and Microsoft's AI4Science, on structural representation/corruption as it pertains to diffusion models, unconditional generation, and inverse materials design. I will highlight current applications, state of the art performance, and discuss challenges and opportunities moving forward.

Abstract: In this talk, I will discuss two connections between particle systems and kinetic theory. On one hand, kinetic theory plays a vital role in characterizing the collective dynamics of interacting particle systems, offering a computationally efficient model. On the other hand, particle methods have seen a resurgence in solving kinetic equations, especially for its potential in high-dimensional settings. I invite you to join me in uncovering the intriguing synergy between molecular dynamics and particle dynamics, all interconnected through the kinetic equations.

Abstract: Large-scale geodynamic processes in the solid Earth often depend intimately on small-scale defects within the constituent minerals. These processes span a wide range of time scales and include convection in the upper mantle, flexure of the lithosphere, glacial isostatic adjustment, postseismic creep, and frictional sliding on faults during earthquakes. Here I describe the influence of dislocations, a particular type of crystal defect, on this range of processes within upper-mantle rocks. The role of dislocations across these timescales is elucidated by a series of laboratory experiments including synchrotron-based experiments to measure yield stress and strain hardening, high-temperature uniaxial tests to investigate anelasticity, and dynamic indentation using ball-drop experiments to assess mineral strength at extreme strain rates. These different experimental approaches are linked through the dynamics of dislocations. The resulting model of dislocation-based deformation resolves conflicts among previous geophysical observations and provides a series of new predictions about the mechanical properties of rocks at both slow and fast timescales not typically accessible in the laboratory. 

Abstract: The transport of waves, such as light and sound, can be radically transformed when waves interact with metamaterial structures with engineered subwavelength features. My group aims to understand and develop electromagnetic and acoustic metamaterials that can control wave-matter interactions in ways that are impossible with conventional materials. In the first part of my talk, I will present our work on acousto-mechanical metamaterials that can steer ultrasonic waves for contactless and programmable actuation. This versatile concept enables new actuation functions, including autonomous path following and contactless tractor beaming, that are facilitated by anomalous ultrasonic scattering and are beyond the limits of traditional wave-matter interactions. In the second part, I will discuss how the same ideas naturally carry over to optical systems. Light is a powerful tool to manipulate matter, with concepts such as optical traps and tweezers widely used across biology and bioengineering to microfluidics and quantum sensing, but typically limited to small objects and short distances. In contrast, our approach to designing nanoscale elements to control the momentum of light could open new frontiers in optomechanics such as macroscale optical levitation and long-range optical actuation. These concepts of nanoscale light-matter interactions could lead to ultralightweight and multi-functional structures and coatings with unique new terrestrial and space applications.

Abstract: Flow control is the notion of manipulating the evolution of a fluid flow to achieve a desired outcome using passive or active means. Flow control technologies can enhance performance and efficiency in engineering systems, ranging from airplanes to underwater robots to wind turbines. Ongoing efforts aim to improve the reliability and performance of these systems by “feeding back” sensed information about the evolution of a flow to determine how to actuate the flow in an optimal manner. Achieving effective flow control often requires reliable and efficient models for the complex dynamics of fluid flows; estimators that can infer knowledge about the evolution of these flows from a limited set of sensor measurements; and control policies and algorithms that use these inferences to actively and reliably manipulate the evolution of fluid flows to achieve specified performance objectives. This talk will provide an overview of past and ongoing research related to the various modeling, analysis, and design challenges associated with controlling flow interactions in aerodynamic systems. Focus will be given to how control theory, system dynamics, optimization, and applied mathematics can be used to reveal essential flow interactions and harness them to achieve a performance benefit.

Abstract: Groups of linear operators are encountered often in mathematical physics. For example, in linear elasticity theory the fourth-order elasticity tensor, relating stress and strain, is restricted to a particular material symmetry group (a subgroup of O(3), the orthogonal group of dimension 3) by a well-known tensorial invariance relationship. A fundamental problem in elasticity theory, then, is to determine the most general form of such tensors for all symmetry groups of practical interest. Classically, elasticians solve this problem in an ad-hoc fashion. To systematically attack such problems, one must discover and employ Group Representation Theory. At the heart of this theory are the so-called "irreducible representations" or irreps. With this lecture, I aim to help the audience befriend the irreps by (i) presenting their definitions and minimal fundamental properties, and (ii) demonstrating their use to find the general form of the elasticity tensor for a particular material symmetry.

Abstract: Origami has attracted increasing attention for its practical value in diverse fields: architectural design, therapeutics, deployable space structures, medical stent design, antenna design, and robotics. In this lecture we present four topics on origami design: 1) A basic theorem for curved origami design (explained in pictures), 2) A step-by-step description of the group orbit procedure, 3) Curved origami structures discretized by exact piecewise linear origami structures (i.e., both the curved origami structure and its piecewise linear approximation are exactly foldable from a flat sheet), and 4) Application of these ideas to stent design for the treatment of brain aneurysms.

Abstract: How do engineers in a manufacturing corporation apply their technical training to explore, discover, understand, and more importantly, transform knowledge into products to improve life? I will discuss the structures at 3M that foster open innovation, and also some of the work my team has done to uncover physical mechanisms to develop and improve various 3M products from Cubitron II abrasives to Optically Clear Adhesives to VHB Structural Glazing Tapes. We are driven by our belief that behind every phenomenon there are underlying governing principles that can be discovered. I will discuss how curiosity and questioning, followed by a systematic and collaborative approach can lead to depth of understanding. This understanding provides a foundation on which to innovate and create value through development of robust and high-performance products.

Bio: Fay Salmon, Staff Scientist within the Corporate Research Systems Laboratory, works with various divisions in applying modeling to 3M core technologies. Her work centers around developing modeling methodologies, closely integrated with experimental observation, to provide realistic physics-based simulation. She is the lead expert responsible for establishing the comprehensive modeling capabilities at 3M for adhesive performance, abrasive cutting processes, and consumer electronics display behavior. She works closely with 3M’s business divisions providing modeling and testing resources for 3M products to a broad customer base, as well as with academia in developing new modeling technologies.

Abstract: Pairing digital technologies to materials and system research is essential to meet the product needs of rapidly evolving markets. Machine Learning, Automation, First-Principles Modeling & Simulation need to integrate seamlessly with lab & process scale data. These technologies have developed rapidly over the past decades. Traditional new material development processes are relatively slow due to the nature of conducting bench top experiments. To accelerate this process, 3M has democratized select digital technologies through our Model Hub & Materials Informatics Platforms. The field of material informatics is emerging to solve material science related problems using advanced machine learning techniques. In this talk, the speaker will introduce key challenges in traditional materials research and how we develop digital technologies to create new products and apply science to life.

Abstract: Fatigue of superelastic Nitinol in the mixed austenite–martensite state was examined in tension using center-tapered dog-bone specimens. A prestraining procedure, mimicking the load history of a medical device component, was applied prior to cycling: specimens were loaded to a fully martensitic state, unloaded partway into the lower plateau to a mixed-phase state, and then subjected to sinusoidal displacement cycles. Strain maps, obtained using digital image correlation, showed substantial variation in local mean and alternating strains across the gage section. In situ surface imaging using a high-speed camera confirmed crack initiation in a narrow transition zone between austenite and martensite that undergoes cyclic stress-induced martensitic transformation (SIMT). Fatigue life data showed an abrupt transition from high-cycle runouts to low-cycle fatigue failures at a stress amplitude level corresponding to the threshold for activating cyclic SIMT. The fatigue threshold can be estimated from the tensile loading–unloading curve.

Abstract: Small defects are often the cause of fatigue crack initiation and failure. Since the initiation and growth of small cracks is the longest portion of the fatigue life of a component it is also the area where the largest increase in performance and quality can be achieved through better understanding and modeling of the material. The prediction of the defect size along with the measurement and analysis of the small crack growth due to fatigue loading is reviewed. The results provide knowledge and guidance to improve the quality and efficiency of engineering structures. The methods and test results support and improve the modeling and prediction of machine components used in more demanding applications and loading situations.

Abstract: An asteroid collision with Earth, though unlikely, is a possibility that may have serious consequences for life on the planet. This motivates the study of methods by which a projected asteroid collision may be averted. In this talk, an overview of proposed methods of asteroid deflection, including gravity tractors, is given. A new type of gravity tractor consisting of a spacecraft in Keplerian motion about the asteroid is described and its characteristics are compared to existing methods. It is shown that this gravity tractor is generally more efficient in imparting the required change of momentum to the asteroid than, for example, a gravity tractor that is stationary with respect to the asteroid. The increased efficiency translates into an overall smaller launch mass for the spacecraft making such a mission more plausible.

Abstract: In this talk, I will discuss quasi-one-dimensional (1D) materials with helical symmetries, examples of which include nanotubes, nanowires and nanoribbons. Emergent forms of such matter are likely to be associated with strongly correlated and collective electronic effects such as superconductivity, ferromagnetism, Wigner crystallization and Mott insulating states. Due to the morphology of these materials, they are expected to exhibit these properties in manners that are significantly different from bulk phase materials. Moreover, the 1D geometry of these structures offer excellent opportunities for incorporating them as materials in novel quantum, electromagnetic and photonic device applications. Broadly, many of the exotic electronic properties featured by these materials are linked to dispersion less electronic states (flat bands) and a corresponding singular peak in the electronic density of states (Van Hove singularity). In this work, we use symmetry adapted first principles calculations and tight-binding models to investigate the electromechanical properties of a set of realistic 1D materials featuring flat bands. Specifically, two prototypical nanotube and nanoribbon systems, based on Kagome and hexagonal lattice geometries of carbon and phosphorus, are studied.  We show that these nanomaterials host flat bands with quadratic band crossing and that their electronic structures can be classified based on the type of singularities in their Bloch wavefunctions. We also show how mechanical deformations can lead to electronic phase transitions in these structures.

Abstract: The topic of dynamical similarity is a classic topic, apparently known in some way to Archimedes. Motivated by a design of a vertical axis wind turbine, we present a theory of dynamical similarity for mechanical systems consisting of interacting elastic solids, rigid bodies and incompressible fluids. Throughout, we focus on the geometrically nonlinear case. We approach the analysis by analyzing the equations of motion: we ask that a change of variables take these equations and mutual boundary conditions to themselves, while allowing a rescaling of space and time. Whereas the disparity between the Eulerian and Lagrangian descriptions of motion — Eulerian for the fluid, Lagrangian for the elastic or rigid solid — might seem to limit the possibilities, we find numerous cases that apparently have not been identified, especially for stiff nonlinear elastic materials (defined in the lecture). We discuss specific applications. We finish the lecture by addressing the following related question: how would one build on earth a drone or rover that, after rescaling various dimensions and possibly substituting different materials, would behave on the Moon or Mars in a precisely predictable way from its behavior on earth?

Abstract: Shape memory alloys are recently being used for direct conversion of heat to electricity based on first order phase transformation. The main challenge of this type of transformation are the high cyclic reversibility and minimization of hysteresis. The systematic tuning of crystal lattice parameters to achieve improved kinematic compatibility between different phases is a broadly effective strategy for improving the reversibility and lowering the hysteresis of solid–solid phase transformations.

Paradoxical behaviors were seen during phase transformation of zirconia based ceramic oxides in which tuning crystal lattice parameters to near perfect kinematic compatibility results in an unusually high degree of irreversibility. The ceramic sample showed different behavior like jumping and explosively disintegrating.

Phase transformation is accompanied with elastic wave emission. In this talk, I will discuss these paradoxical behaviors by analyzing the stresses developed due to wave propagation during phase transformation and role of phase boundary velocity for 1D case.

Abstract: Multiscale experiments in heterogeneous materials and the knowledge of their physics under shock compression are limited. This study examines the multiscale shock response of particulate composites comprised of soda-lime glass particles in a PMMA matrix using the newly developed full-field high-speed digital image correlation (DIC) for the first time. The high spatial resolution measurement using high speed digital image correlation allowed to measure the spatially resolved velocity profile. Normal plate impact experiments, and complementary numerical simulations, are conducted at stresses ranging from 1.1 − 3.1 GPa to elucidate the mesoscale mechanisms responsible for the distinct shock structure observed in particulate composites. The particle velocity from the macroscopic measurement at continuum scale shows a relatively smooth velocity profile, with shock thickness decreasing with an increase in shock stress, and the composite exhibits strain rate scaling as the second power of the shock stress. In contrast, the mesoscopic response was highly heterogeneous, which led to a rough shock front and the formation of a train of weak shocks traveling at different velocities. Additionally, the normal shock was seen to diffuse the momentum in the transverse direction, affecting the shock rise and the rounding-off observed at the continuum scale measurements. The numerical simulations indicate that the reflections at the interfaces, wave scattering, and interference of these reflected waves are the primary mechanisms for the observed rough shock fronts.

Abstract: Ionic liquids have emerged as a highly promising material class with regard to diverse applications ranging from bio- and electrochemistry to energy storage. A major breakthrough is given by the design of ionic liquid-based soft solids, so-called ion gels, as solid-state and flexible electronic applications incorporating ionic liquids are enabled. While the electronic properties of such ionic liquids and gels have been studied at room temperature, there is little to no temperature-dependent information available that incorporates their first-order phase transitions or thermal history. Here, we examine the first-order phase transition in ionic liquids by performing temperature-dependent structural analysis of the ionic liquid 1-ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([EMIm][TFSI]) and one of its polymer-based ion gel derivatives. We combine our findings with temperature-dependent impedance analysis of the ion gel and demonstrate the successful stabilization of the phase transition. Ultimately, our results emphasize the potential of combining first-order phase transitions and novel material systems in order to unlock new material functionalities.

Abstract: Conventional rigid robotic manipulators are well understood and have widespread use in applications ranging from autonomous manufacturing to flight simulator platforms.  Robotic systems that are driven by cables are relatively new and have intriguing features, including larger workspaces and higher payload-to-weight-ratios, which enables exciting new robotic applications.  While these features are promising, performing high-acceleration maneuvers that take advantage of these properties is challenging and can even cause instability of the system due to the presence of elasticity in the cables if not accounted for correctly.

This talk will present an overview of my research group's work on the control of cable-driven flexible robotic systems. It will begin with an entry-level tutorial on robust control theory and how we use it to obtain mathematical guarantees of stability when working with flexible robotic systems. An overview of the modular reduced-order dynamic modeling approaches developed by my research group will also be presented, where robotic systems with any number of cables and arbitrary geometric configuration can be accommodated. If time permits, a brief description of the sensing and estimation framework we have formulated for these systems will be discussed.

Abstract: Constitutive modeling and large-scale simulation remain challenging due to the inherent complexities of materials such as inelasticity and heterogeneities. Surrogate modeling has been popularized as a promising alternative to full-scale simulation in complex engineering processes. This talk will survey our recent research on developing hybrid computational methods by combining physics-based mesh-free numerical models and data-driven dimensionality reduction techniques to address various difficulties in computational mechanics arising from material modeling, characterization, and reduced-order modeling. The proposed methods will be demonstrated on examples related to mechanical, biomechanics, and geophysical applications.

I will first talk about the development of reduced-order models for a nonlinear thermomechanical problem based on manifold learning together with sparse sampling. This hyper-reduction method is used for fast prediction of thermal fatigue behaviors of electronic packages. Second, by introducing manifold learning to the constitutive model component, we propose a physics-constrained data-driven modeling approach under the Galerkin meshfree framework, which enables predictive physical simulation directly from material data without the employment of phenomenological constitutive models. Lastly, I will discuss our recent work on developing a novel hybrid FEM/neural-based surrogate method for coupled systems with the application of ice-sheet modeling.

Abstract: The Phase Field Crystal (PFC) model is a versatile approach to study the dynamics of defected crystalline materials in terms of kinematics and kinetics of dislocations, grain boundaries and fracture dynamics. The PFC model has minimal assumptions based on representing a crystal lattice symmetry by an order parameter that minimizes an appropriate free energy at equilibrium, and that relaxes diffusively in out-of-equilibrium conditions. In this formalism, lattice defects and their properties are determined by the PFC free energy and the dynamics of the order parameter. A challenge with this description is to model dislocation dynamics in the presence of elastic fields and connecting that with continuum elasticity and plasticity descriptions.

In this talk, I will present a general method to identify dislocations in the crystal order parameter and derive expressions for the dislocation density tensor and its dynamics in terms of the evolution of the order parameter. The general expression of the dislocation velocity reduces, under certain approximations, to the overdamped motion driven by the Peach-Koehler force with a mobility determined by equilibrium properties. By extracting the stress tensor in the crystal from the order parameter, we are able to constrain the classical PFC dynamics to mechanical equilibrium. These methods have been used to study the shrinkage of a shear dislocation loop in a bcc lattice which shows that this process depends heavily on the state of stress in the crystal.

Abstract: Quantum chemical calculations using density functional theory (DFT) are now commonplace in materials science. There are several publicly available materials databases (Materials Project, OQMD, AFLOW, JARVIS, etc.) that house DFT calculation results for millions of inorganic crystals. One of the tabulated properties for each calculation (structure) is the DFT-calculated total energy, which can eventually be used to ascertain whether a given inorganic structure is thermodynamically “stable”. Thermodynamic stability plays a central role in determining whether a hypothetical material can be realized experimentally, and its calculation should be considered carefully. This talk will discuss various aspects of thermodynamic stability calculations such as: why we should care about them, how to perform them with DFT, differences between DFT- and ML-based stability predictions, and the limitations of stability calculations for accelerated materials discovery.

Abstract: The study of crystallography as a system of classification for experimentally determined crystal structures dates back to at least 1912, with the first standardized crystallography tables being published in 1935. Such tables are the de facto common language for materials scientists to describe the microscopic structure of crystalline solids. On the other hand, in the field of atomistic modeling, we deal directly with the coordinates of every particle and often have little exposure to the concepts and notation of crystallography.

In this educational seminar, I will introduce crystallography from this point of view. At the KIM Project, we are currently developing a testing framework that automatically computes the property predictions of interatomic potentials applied to arbitrary crystal structures. In order to classify and archive this massive number of possible structures, we have adopted the AFLOW crystal prototype designation, which is a concise and complete description of any bulk crystal based on the conventions found in the International Tables for Crystallography. Using this motivating example, I will cover the basic language of crystallography, describe how to construct a unit cell of a crystal from its space group and Wyckoff positions, and address common points of confusion. Using these concepts, I will describe the aforementioned testing framework and its use of AFLOW software for classifying and generating coordinate files for arbitrary crystals.

Abstract: Reduced order models (ROMs) are a highly efficient alternative to full-order finite element models (FEM) of geometrically nonlinear structures. Many non-intrusive reduced order modeling methods have been developed over the decades to serve as a digital twin of geometrically nonlinear structures, providing accurate dynamic simulations with dramatically reduced computational cost. However, the ROM methods pose some critical issues. The existing methods are sometimes not reliable, and so expensive simulations must be run to check the accuracy and optimality of the ROMs before they can be used confidently. Also, a ROM is typically only valid for a single FEM and does not account for variations in the FEM. Thus, if the design of the structure changes so that the FEM changes in some way, one must recompute the corresponding ROM with a new set of static load-displacement solutions. This also greatly increases the cost of analysis using ROMs, making them less attractive. This study proposes a new data-driven reduced order modeling method for geometrically nonlinear structures, which can resolve these issues while keeping the computational cost reasonable. In particular in this talk, a new data-driven reduced order model based on Gaussian process regression (GPR) will be proposed. The data-driven GPR ROM accurately captures how the ROM coefficients change as the FEM is changed, so that one GPR ROM can predict the behavior of a wide range of systems and also quantify its predictive confidence. This work also opens up new possibilities for efficient and reliable model updating of geometrically nonlinear structures. In this respect, an application of a data-driven ROM to FE model updating (FEMU) is explored. The proposed updating method incorporates a GPR ROM into the model updating procedure, allowing one to use a single GPR ROM to efficiently update the FEM parameters to match actual field data. The computational cost of model updating could be significantly reduced compared to conventional FEMU approaches at the cost of preparing a well-trained data-driven ROM.

Abstract: Optimal design is a powerful methodology where the design of a structure is first posed as an optimization problem and then subsequently solved computationally. It can realize structures of unprecedented performance, far exceeding that which can be achieved by traditional intuitive-based design. Additionally, with the recent advances in additive manufacturing technologies, these designs may be fabricated in a practical setting. However, many issues arise on both the theoretical and computational front, especially when accounting for complex physics and manufacturing constraints. In this talk, I address some of these issues while discussing my work on optimal design of both impact-resistant structures and soft responsive actuators.

We begin by introducing optimal design through the canonical example of compliance minimization of a linear elastic structure. We examine the conventional methods used to regularize and solve the optimization problem. However, in cases with more complicated material models or more stringent manufacturing constraints, these methods may not be sufficient. We will explore two such examples.

First, we consider the design of structures for impact resistance. Here, transient dynamics, rate-dependent plasticity, and material failure must be accounted for in the mechanics modeling. Thus, we consider a J2 plasticity model enriched with phase-field damage. Gradient-based optimization methods repeatedly update the design, requiring forward simulation and sensitivity calculation at each iteration. For this, we develop a novel computational method to efficiently compute the dynamic trajectory by splitting the non-linear and non-local coupling of the damage operator through an augmented lagrangian formulation. Then, we apply the adjoint method to compute design sensitivities in a similar manner. We consider two examples. The first is the design of solid-void structures for blast loading. Then, we explore the trade-offs between strength and toughness to design spall-resistant structures undergoing impact.

Next, we investigate the design of soft responsive actuators. Recent developments in material synthesis and 3D printing of anisotropic materials, such as liquid crystal elastomers, have facilitated the realization of structures with arbitrary morphology and tailored material orientation. Thus, we look to optimize structure and material orientation for integrated structures composed of both passive and active materials. However, the manufacturing process constrains the design as extrusion-based 3D printing aligns nematic directors along the print path. We discuss the proper regularization in this setting and formulate the design with such constraints. We consider a variety of lifting actuators, where we realize manufacturable designs while also recovering the print paths.

Finally, I discuss some areas of interest and research directions in the field moving forward.

Abstract: The CSL/DSCL model for interfaces in crystalline materials offers a unified framework to study interface dislocations in diverse materials systems, such as phase boundaries, grain boundaries, and two-dimensional (2D) heterostructures. Central to this model are the two lattices — coincident site lattice (CSL) and the dis- placement shift complete lattice (DSCL) — derived from the two lattices that constitute an interface. The CSL and the interface dislocations in 2D heterointerfaces are commonly referred to as the moire ́ superlattice and strain solitons, respectively. The CSL/DSCL model relies on the existence of a coincidence relation between the two lattices that meet at an interface. The model’s ability to quantitatively predict the thermodynamics and kinetics of interfaces has been demonstrated for a limited set of symmetric tilt grain boundaries (STGBs) in cubic materials and twin boundaries. However, the lack of a general framework of interface defects prevents its applicability to arbitrary rational grain and phase boundaries, and 2D heterostructures.

In this talk, we present a mathematical framework based on the Smith normal form (SNF) for integer ma- trices to study the bicrystallography of a crystal interface. One of the main results of the framework is the characterization of interface dislocations based on the translational symmetry of the interface. The translational symmetry follows from a constructive proof of the invariance of the CSL/moire ́ under discrete relative displace- ments of the parent lattices by a DSCL vector. In addition, we obtain necessary and sufficient conditions on the two lattices, related by not only rotations but also lattice distortions, for the existence of a CSL/moire ́.

We will demonstrate the application of SNF bicrystallography to a) enumerate disconnection modes in arbitrary rational grain boundaries, including glide and non-glide modes in both symmetric- and asymmetric- tilt grain boundaries, and b) to study interface dislocations in bilayer graphene with a significant twist (> 10◦). The constructive nature of the framework lends itself to an algorithmic implementation based exclusively on integer matrix algebra.

Abstract: Superconductivity has been a major research topic for more than a century, yet in many important materials this macroscopic quantum phenomenon remains poorly understood. We have uncovered that superconductivity emerges in an unusual, yet remarkably universal manner upon cooling in three well-known families of complex oxides – strontium titanate, strontium ruthenate, and the cuprates – for which the origin of superconductivity is thought to differ [1]. From complementary diffuse neutron and x-ray scattering measurements, we uncovered evidence that this universal electronic behavior is caused by intrinsic correlated structural inhomogeneity that must be inherent to the oxides’ perovskite-based crystal structures [2]. The prevalence of such inhomogeneity has far-reaching implications for the interpretation of electronic properties of perovskites in general, including thin films and heterostructures. In the case of the cuprates, this constitutes a pivotal part of a robust phenomenological model that comprehensively captures hitherto elusive properties of the normal and superconducting states [3]. In the case of strontium titanate, these insights motivated a systematic study of plastically deformed crystals and led to the discovery of remarkable superconductivity and ferroelectricity enhancements associated with the self-organization of dislocations into periodic structures [4].

[1] D. Pelc et al., Nat. Commun. 10, 2729 (2019)
[2] D. Pelc et al., arXiv:2103.05482
[3] D. Pelc et al., Sci. Adv. 5, eaau4538 (2019); Phys. Rev. B 102, 075114 (2020)
[4] S. Hameed et al., Nat. Mater. 21, 54 (2022)

Abstract: The focus of this talk is an inclusive paradigm for the homogenization of wave motion in periodic media (including the source term) at finite frequencies and wavelengths. We take the eigenvalue problem for the unit cell of periodicity as a point of departure, and we consider projection of the germane Bloch wave onto a suitable eigenfunction (i.e. “phonon”) basis as the descriptor of effective wave motion. For generality, we consider the junctures of dispersion branches and dense clusters thereof, where the asymptotic analysis reveals several distinct regimes driven by the parity and symmetries of the eigenfunction basis. In the case of junctures, one of these asymptotic regimes is shown to describe the so-called Dirac points that are relevant to the phenomenon of topological insulation. On the other hand, the “dense cluster” model is found to invariably entail a Dirac-like system of equations that paints the interacting dispersion surfaces as blunted cones. The analysis is established in a generic setting, assuming periodic continua with or without “perforations” that are supported by an arbitrary Bravais lattice. We extend the foregoing framework to the analysis of discrete, origami-inspired structures and demonstrate that the so-homogenized model inherently provides both macro- and micro-scale description of the relevant wave motion. The talk concludes with an application of the “dense cluster” model toward explicit evaluation of the Berry phase in 2D periodic continua. We expose the conditions under which the latter (geometric phase) quantity — that is one of the pillars of the emerging field of topological mechanics — is quantal and topological, and provide the formula for its single-wavenumber evaluation.

Abstract: Many interesting and important processes in molecular systems such as protein folding, the transition of liquid-to-solid and chemical reactions involve overcoming free energy barriers. Often the free energy barriers are large, and this makes it almost impossible to sample these processes through straightforward molecular dynamics simulations. Consequently, several methods have been developed to address this limitation. In our research, we use a family of methods called path sampling techniques. We Have integrated data science methods and path sampling techniques to enable large-scale simulations of the molecular processes of interest. In addition, we are using machine learning approaches to better understand the data generated from these calculations. In my talk, I will discuss existing challenges in studying these important yet hard-to-sample molecular processes, our ongoing work to address these challenges, and the application of these methods to studying nucleation of ice and gas hydrates.

Abstract: Single layer/ultrathin MoS2 is being increasingly sought for composites, semiconductors, and catalysts applications. To meet up the demand, more scalable production methods are being actively researched. One such promising method is micromechanical exfoliation of bulk MoS2 crystals. High frequency ultrasonic bombardment is found to generate shearing at nanometer scale, and is capable of exfoliating MoS2 in large quantities. The role of the solvent was found crucial to the process, as the appropriate solvent maximized the concentration of nanosheets and stabilized the dispersion. The exact molecular mechanism of solvent stabilization is still debated, with major emphasis on phenomenological models like surface energies matching using the empirical Hansen parameter. In this seminar I shall discuss the role of the solvent / ligand in stabilizing MoS2 nanosheets in both aqueous and non-aqueous media from experimental NMR studies in tandem with classical Molecular Dynamics (MD) simulations to provide a Molecular perspective of the role of the solvent in stabilizing MoS2 nanosheet dispersions.

Suitable solvent systems include aqueous ionic surfactant solutions and certain organic solvents like N-Methyl-2-pyrrolidone (NMP). The ionic surfactant dispersions are stabilized by electrostatic repulsion between the sheets. Using 2D nuclear Overhauser effect (NOESY) spectroscopy it is shown that the surfactant chains are weakly bound and adsorbed randomly on the surface of the MoS2 nanosheet, undergoing rapid exchange. Classical MD simulations of dispersions provide a molecular interpretation of the NMR results and stability of the dispersion. MD simulations when combined with DLVO theory also provide semiquantitative insights in stabilization and aggregation behavior of the colloid. In non-aqueous regime, NMP is one of the most efficient solvents for the exfoliation of MoS2. It is shown that trace water present in NMP is crucial for the stability of MoS2 nanosheets in NMP dispersions. In the absence of water the sheets are fragmented and chemically unstable. Using experimental NMR and TEM measurements, supported by classical molecular dynamics simulations, the role of water molecules in stabilizing the dispersion is established. The water molecules are shown to localize at the Mo-terminated edges of the MoS2 sheets thereby inhibiting chemical erosion of the sheets and also exhibit enhanced interactions with the solvent NMP molecules leading to the stability of the dispersion.

Abstract: Numerical branch following techniques are employed to efficiently determine solution paths of non-linear systems as a parameter is varied.  For equivariant equations, solution paths with nontrivial symmetry lie within an invariant subspace, called the fixed point space.  At symmetry-breaking bifurcation points, the Jacobian becomes singular.  Conveniently, this singularity is orthogonal to the fixed point subspace and one can construct the symmetry reduced problem on the fixed point space to solve a lower dimensional system of equations without singularity.  However, in practice the explicit construction of the reduced problem is computationally prohibitive for many problems of interest.  As an alternative, we are investigating algorithms that operate on the complete space but exploit symmetry information to improve their efficiency.  In this context, Krylov methods are attractive because they will naturally work within the fixed point space.  The robustness of such algorithms must be carefully considered because their numerical implementation (using floating-point math) may lead to departures from the fixed point space that could adversely affect convergence near singular points.  This work considers the implications of using Krylov-based solvers (e.g. GMRES) in the typical Newton-Raphson corrector step of branch following algorithms for symmetric systems.  Specifically, the behavior of Krylov solvers at both regular and singular points (e.g. symmetry-breaking bifurcation) is addressed and the efficiency of these solvers is compared to that obtained with reduction methods. This talk will include discussions of efficiencies in leveraging symmetry in different ways for numerical solutions of these problems.

Abstract: Many natural and artificial heterogeneous structures that can be modeled as a thin layer on a substrate are susceptible to surface instabilities such as wrinkling and folding among others. A key feature present in these systems is the occurrence of bifurcation of solutions from a parent state.

The mathematical treatment of these problems in the post-bifurcated range is cumbersome due to the numerically ill-conditioned operators involved, the number of degrees of freedom required and the complex nature of the branches in equilibrium. These difficulties make the two fundamental tasks of the post-bifurcation analysis, the determination of bifurcation points and switching between equilibrium paths at bifurcations, very challenging.

Probably to avoid the use of asymptotic analysis, which produces local results, a number of methods that rely on adding imperfections to the system have been proposed. These methods are adopted to "predict" the equilibrium configurations of interest, but the techniques are not of general application. Another observation that has left researchers puzzled is noticing that two different configurations may have the same energy in the bifurcated state. We claim that most of the preceding difficulties and doubts can be mitigated, and even eliminated, by employing a group theoretic framework.

In this work we describe the aforementioned framework and apply it to the simplest model of a thin layer on a substrate, the inextensible Euler-Bernoulli beam on a nonlinear foundation, under axial compression. We illustrate the advantages of the framework when compared to conventional methods; determine the global bifurcation diagram for a specific window of load and deformation, including all the bifurcating branches allowed by the equivariant branching lemma for particular symmetries; and explore the influence of local mechanical properties on the post-bifurcated range.

Abstract: Objective Molecular Dynamics (OMD) is a generalization of periodic MD which exploits the invariance of the equations of MD and the underlying potential energy hypersurface. The method enables forging of rigorous links between fundamental quantum mechanics and nonstandard macroscopic continuum mechanics since it provides us an atomistic analogue of motions that are exact solutions of the macroscopic equations. The other advantage is that in OMD only a few atoms are actually simulated, but the full infinite set of atoms satisfy exactly the MD equations. This considerably reduces the computational cost of the problem.

Here, we apply the method to investigate the breakdown of Navier-Stokes-Fourier (NSF) equations under strong gradients by examining the OMD flows of Lennard-Jones argon gas. We propose the extended hydrodynamic Rivlin-Ericksen (RE) theory based higher order constitutive model which make significant improvements over NSF relation in capturing non-linear momentum transport. This work finds application in facilitating the use of continuum CFD modeling even in the regime of far-from-equilibrium flows which will be highly useful for the modeling of vehicle scale hypersonic and micro-nano scale flows.

Next, we apply the same method to investigate a very different system than the previous case. We study mechanism of cross-slip where screw dislocation leaves its habit plane and glides in a conjugate "cross-slip" plane. We try to answer that how large a stress can FCC nickel sustain before it cross-slips in non-equilibrium regime under the effect of large strain rate at finite temperature by taking a kinetic viewpoint. This finding can assist the modeling of cross-slip at the mesoscopic scale within the framework of dislocation dynamics simulation under shock loading conditions. We also report some important pathways which material chooses to relax the stress under different loading conditions.

Abstract: Recently, changing political and environmental demands are being met by an intense growth of research on efficient, environmentally friendly and ecological technologies. Among these technologies, lead-free ferroelectric ceramics have been widely studied, as possible applications range from the substitution of lead-based materials in piezoelectric devices and innovative cooling technologies to energy harvesting and conversion applications. However, their full potential remains unexploited for both bulk materials and thin films, the latter being a major driving force in today’s key technology sectors. In this context, the ferroelectric potassium sodium niobate (KNN) ceramic is assumed to bear great potential ever since its discovery in the 1950’s due to its combination of material properties i.e., its perovskite structure and correlated first-order phase transformations and ferroelectricity, as well as its high Curie temperature. However, composition and microstructure control are major challenges due the material’s multi-scale chemical heterogeneity, including high volatility, as well as varying diffusion constants and leading to an insufficient electrical performance as compared to lead derivatives.

The focus of this work is on the analysis, optimization and theory-guided synthesis of KNN, based on the geometrically nonlinear theory of martensite (GNLTM).  The latter gives precise rules for the minimization of structural fatigue, but its applicability to complex ceramic materials is unclear.  For KNN a major goal is the suppression of abnormal grain growth and the bimodal grain size distribution that lead to degradation of thermal and electronic properties. We show that the GNLTM correctly models favorable lattice structures and thus improved material properties for the homogeneous ceramic in which abnormal grain growth has been successfully suppressed. We achieve excellent thermal stability and repeatability of the tuned ceramic as seen from temperature-dependent X-ray diffraction (XRD), transmission electron microscopy (TEM), and energy dispersive X-ray spectroscopy (EDS). These investigations reveal that the GNLTM together with advanced synthesis and characterization techniques provides a useful strategy for the improvement of the reversibility and functionality of phase-change materials with complex chemistry and structure.

Abstract: Many natural and artificial heterogeneous structures that can be modeled as a thin layer on a substrate are susceptible to surface instabilities such as wrinkling and folding among others. A key feature present in these systems is the occurrence of bifurcation of solutions from a parent state.

The mathematical treatment of these problems in the post-bifurcated range is cumbersome due to the numerically ill-conditioned operators involved, the number of degrees of freedom required and the complex nature of the branches in equilibrium. These difficulties make the two fundamental tasks of the post-bifurcation analysis, the determination of bifurcation points and switching between equilibrium paths at bifurcations, very challenging.

Probably to avoid the use of asymptotic analysis, which produces local results, a number of methods that rely on adding imperfections to the system have been proposed. These methods are adopted to "predict" the equilibrium configurations of interest, but the techniques are not of general application. Another observation that has left researchers puzzled is noticing that two different configurations may have the same energy in the bifurcated state. We claim that most of the preceding difficulties and doubts can be mitigated, and even eliminated, by employing a group theoretic framework.

In this work we describe the aforementioned framework and apply it to the simplest model of a thin layer on a substrate, the inextensible Euler-Bernoulli beam on a nonlinear foundation, under axial compression. We illustrate the advantages of the framework when compared to conventional methods; determine the global bifurcation diagram for a specific window of load and deformation, including all the bifurcating branches allowed by the equivariant branching lemma for particular symmetries; and explore the influence of local mechanical properties on the post-bifurcated range.

Abstract: The material potassium sodium niobate is considered one of the most prominent material systems in line to substitute toxic lead-containing ferroelectric materials. It exhibits first-order phase transformations and ferroelectricity providing for possible applications ranging from energy conversion to innovative cooling technologies, hereby addressing some of the most urgent challenges of modern societies. However, a major obstacle in the application of potassium sodium niobate is its multi-scale heterogeneity and the correlated lack of understanding of its phase transition dynamics. This can be seen from the findings of Pop-Ghe et al. which reveal the occurrence of intermediate twinning during the phase transition. Here we show that intermediate twinning is a result of an energy minimization problem. We study energy minimizing deformations of a macroscopic continuous elastic energy function representing the multiwell structure of the crystal. The continuous energy is linked to the discrete lattice through the Cauchy-Born hypothesis. The construction of the minimizers is based on compatibility conditions which ensure continuous deformations with discontinuous deformation gradients.  Minimizing solutions agree with the experimental observations, forming laminates between the tetragonal variants under the cubic to tetragonal transformation and also crossing twins under the tetragonal to orthorhombic transformation.

Abstract: The Quasi-1D materials such as helical nanotubes are attracting extensive attention due to their exotic electronic properties, and strongly correlated effects such as flat bands, ferromagnetism, ferroelectricity, and superconductivity. The ability to extend these structures into long wires offers a great opportunity for various technological applications. In this talk, I will discuss two different methods used for predicting these functional properties in these structures. First, I will present the empirical Tight Binding (TB) calculations for computing dispersion behavior of Graphene, Kagome lattices, and nanotubes. Second, we build a computational framework that allows studying helical nanotubes using ab-inito Density Functional Theory (DFT) and Hartree Fock (HF) method. In our preliminary study, we observe a structure that offers very unusual behavior where both flat bands and Dirac cones occur simultaneously. However, the single-electron theories do not capture the exact physics of strongly correlated methods. Methods such as coupled-cluster theory and Density Matrix Renormalization Group which consider many body effects are also discussed.

Abstract: Most origami structures and much of recreational origami are designed as piecewise rigid origami. In some cases, it would be desirable to allow smooth, nonaffine isometric deformations of the tiles, for example, when one wishes to build in some elastic energy that would bias the structure toward some particular configuration so that the structure would tend to return to that configuration upon release. Additional possibilities would arise for functional isometrically deforming tiles, such as shape memory tiles. From the perspective of continuum mechanics to describe isometric deformations and formalize the compatibility conditions at the folds, we present a theory for making isometric origami with curved folds and a method based on the group theory for constructing complex isometric origami. Some potential applications, such as vertical-axis wind turbines, have also been studied.

Abstract: Two-dimensional (2D) materials are attracting considerable attention for their mechanical, electrical and optical properties. In particular the ability to change the properties of 2D materials through stacking and deformation, referred to as "strain engineering," offer great opportunities for advanced nanodevice applications. In this talk, two different examples of strain engineering will be discussed. First, is a simple experimental approach to introducing strain into multilayer flakes of molybdenum disulfide (MoS₂) by float-capturing the flake onto a holey silicon nitride substrate. Through atomistic simulation and continuum mechanical modeling, we show that the Voronoi tessellation bend contour pattern observed in the experiments is driven by localized couples at the substrate hole edges. The limitations of continuum theory in modeling the bending of MoS₂ layers are discussed. Second, we discuss preliminary results related to dynamic reconstruction in twisted graphene bilayers. The transition from an initial incommensurate structure to commensurate domains occurs through a nucleation process followed by wave propagation and merging. The dynamics of this process are studied through atomistic simulation and continuum modeling.

Abstract: Ionic crystals such as solid electrolytes and complex oxides are central to modern technologies for energy storage, sensing, actuation, and other functional applications. An important fundamental issue in the atomic and quantum scale modeling of these materials is defining the macroscopic polarization. In a periodic crystal, the usual definition of the polarization as the first moment of the charge density in a unit cell is found to depend qualitatively – allowing even a change in the sign! - and quantitatively on the choice of the unit cell.

We examine this issue using a rigorous approach based on the framework of two-scale convergence. By examining the continuum limit of when the lattice spacing is much smaller than the characteristic dimensions of the body, we prove that accounting for the boundaries consistently provides a route to uniquely compute electric fields and potentials despite the non-uniqueness of the polarization. Specifically, different choices of the unit cell in the interior of the body leads to correspondingly different partial unit cells at the boundary; while the interior unit cells satisfy charge neutrality, the partial cells on the boundary typically do not, and the net effect is for these changes to compensate for each other. Broadly, the view advocated in this work is in the spirit of classical continuum mechanics; the polarization field is a multiscale mediator that captures some information from the atomic level, and one can take any choice as long as consistent transformations between energy, kinematics, and boundaries are respected. The immediate analog in continuum mechanics is the freedom in the choice of reference configuration and the corresponding value of the deformation field and strain energy density response function as long as care is taken to define suitable transformations between different choices.

Abstract: Transport phenomena play an important role in designing and engineering materials with tailored functionalities. This is especially true for materials with reduced dimensions. Thermal conductivity and interfacial thermal conductance, as basic transport properties of materials and interfaces, can provide a wealth of information on the fundamental scattering processes of charge and thermal carriers with structural defects, boundaries, and interface imperfection. In this talk, I will share our group’s recent progress on utilizing state-of-the-art ultrafast optical metrology to study the thermal and magnetic properties of functionalized materials spanning a wide range of applications. This will include: (1) creating the ultralow thermal conductivity using single crystals of correlated perovskite oxides; (2) revealing the 3D anisotropic thermal transport in black phosphorus, as the next-generation of “wonder materials” for the semiconducting industry; (3) engineering interfacial thermal transport across the solid-solid interface between sapphire and polystyrene, and across the solid-liquid interface between functionalized nanoparticles and water; (4) developing low-damping and high-thermal stability materials with perpendicular magnetic anisotropy for spintronic applications. Last but not least, I will highlight our recent work on manipulating spin precession using optically launched acoustic strains at ultra-high frequencies (~60 GHz). The structure-property relationships of functional materials revealed by the ultrafast pump-probe technique opens up opportunities of tailoring material properties by structural engineering at the atomic and molecular levels. Ultimately, such an understanding can be leveraged to guide the design and optimization of materials, as promising building blocks for high-performance electronic devices, thermal management, solid-state energy conversion, and hard-disk data storage

Abstract: In this talk Jiacheng and Selim will give an overview of two projects ongoing at the Robotic Sensors Networks Lab (http://rsn.cs.umn.edu). Jiacheng will introduce velcro peeling as a representative application for robotic manipulating of non-rigid objects in complex environments. He will present our recent work on designing strategies for peeling velcro strips placed on various surfaces such as planes and cylinders. Specifically, the problem will be formulated as a Partially Observable Markov Decision Process and solved using a multi-step deep recurrent network for the cases of tactile-only and visual feedback. Simulation and a real experiment setup will be used to validate the strategies and compare them against benchmark strategies.

Selim will give an overview of our recent work on environmental monitoring. In particular, he will present a recent result on the following problem: Consider a mobile robot tasked with localizing targets at unknown locations by obtaining relative measurements. The observations can be bearing or range measurements. How should the robot move so as to localize the targets and minimize the uncertainty in their locations as quickly as possible?

Abstract: In 1914, a magnetic alloy with an unusually high magnetic permeability and low coercivity was discovered at the Bell Telephone Laboratories. This magnetic alloy resulted from a series of investigations on the iron-nickel alloy system, in which the nickel content and manufacturing conditions, such as heat treatment, magnetic annealing and mechanical loads, were systematically varied. Under a very specific combination of the alloy composition (78.5% nickel content) and manufacturing conditions, the magnetic alloy (now known as the permalloy) demonstrates a drastic increase in the magnetic permeability and a decrease in coercivity. In the past, this unusual behavior of the permalloy has been attributed to the anisotropy constant, however, there is still no theory that explains this drastic decrease in coercivity in magnetic alloys. Our goal is to identify the relation between the magnetic material constants that is key in reducing magnetic coercivity. We hypothesize that a combination of a large local disturbance (material microstructure) and material properties, such as anisotropy coefficient and magnetostriction coefficients, contribute to the drastic decrease in coercivity in magnetic alloys. We formalize this idea using the micromagnetics theory in a phase-field framework and use energy minimization methods to investigate the links between microstructures and material constants in nickel-iron alloys. Our results demonstrate agreement with the permalloy experiments and provide theoretical insights into developing magnetic alloys with small hysteresis.

Abstract: The proliferation of focused ion beam (FIB) microscopes has had a profound impact on nanoindentation-based testing, allowing the fabrication of site-specific, small-scale structures for mimicking more classical mechanical tests. Furthermore, many such nanoindentation-based tests are now carried out within in situ environments, such as in electron microscopes and at synchrotron beam lines such that the evolution of heterogeneous deformation can be directly correlated to load-displacement response. Much attention has been focused on microcompression testing, where the nearly universal observation that smaller is stronger has helped, in part, to solidify previous observations of indentation size effects. More recently, micron-scale tensile testing and microbeam bending experiments have also coupled the ease of FIB fabrication with the high-resolution measurements afforded by nanoindentation instrumentation. So in addition to studying the influence of finite volumes on plasticity, site-specific mechanical tests on engineering materials - where bulk counterparts may not even exist - allow insight into the fundamental characteristics governing deformation and fracture in structural components. In the present talk I will provide an overview of this broad spectrum of micromechanical testing methods which couple FIB-milled samples with nanoindentation instrumentation, focusing on two case studies. In the first example, the influence of structural geometry on the elastic response of nanoporous gold highlights the importance of high spatial resolution 3D reconstruction data to understanding mechanical behavior of materials. The second example explores the insight into fracture of technical alloys achieved through microbeam bending experiments of individual grain boundaries.

Abstract: First principles calculations that rely on no experimental input has been an integral part of solid state materials science during the past decades. Density Functional Theory (DFT) in combination with standard approximations such as the local density approximation (LDA) is the workhorse of first principles materials studies because of its relatively low computational cost, as well as its surprising accuracy in reproducing and predicting certain quantities. However, not only do approximations such as LDA introduce quantitative errors into DFT, but the most commonly used DFT approach, the Kohn-Sham DFT, also has fundamental shortcomings which makes is qualitatively insufficient in capturing phenomena such as paramagnetism.

In this talk, after a short review of DFT, I am going to introduce a state of the art method, DFT+Dynamical Mean Field Theory (DFT+DMFT), which has been developed to reproduce correlated electronic phases. I am going to review some recent practical developments in the theory and implementations of DFT+DMFT, and show how it perform superior to Kohn-Sham DFT in reproducing the crystal structure and excitations (phonons) of 3d transition metal compounds. Specific examples I will cover will include transition metal oxides as well as elemental systems like iron.

Abstract: Being one of the major incentives in advancing technologies, characterizing the phase transformation in materials is yet far from reaching a fully comprehended subject. Understanding the mechanics, thermodynamics, and kinetics of the phase transformation serves a significant role in modeling the performance of materials. In this talk, we introduce a non-destructive in situ method for monitoring the advancement of the reaction front with a resolution of ~10 nm. We combine Picosecond Ultrasonics with Atomic Force Microscopy to study the velocity of the phase boundary propagation and the corresponding volumetric strain. Picosecond Ultrasonics is a pump and probe technique that can measure the thickness of the internal layers of material using ultrasounds that are generated and detected optically. Crystalline silicon is chosen as our model system due to its characteristic phase transformation behavior during its reaction with lithium. Using this technique, we have examined the diffusion of lithium atoms through different crystallographic orientations under various galvanostatic and potentiostatic conditions. Based on these experimental results, we have calibrated a modified Cahn-Hilliard type of phase field model of a moving phase boundary problem. In contrast to the classical formulation, the mobility of the interface can be determined using this modified Cahn-Hilliard model. The relevant thermodynamic and kinetic parameters for the phase transformation due to diffusion of Li in crystalline Si for the two crystallographic orientations are extracted. The extracted model parameters can facilitate the simulation of phase transformation in more complex structures with multiple crystallographic facets.

Abstract: A phase of matter is a useful to build our understanding of materials.  I will review two key ways that symmetry can distinguish phases of matter: the "conventional" Landau picture of spontaneous symmetry breaking, and a more recent picture connected to topology.  I will give examples of how this understanding has allowed us to predict interesting new material properties.

Abstract: Architected materials have been ubiquitous in nature, enabling unique properties that are unachievable by monolithic, homogeneous materials. Inspired by natural processes, man-made three-dimensional (3D) architected materials have been reported to enable novel mechanical properties such as high stiffness- to-density ratios or extreme resilience, increasingly so when nanoscale size effects are present. However, most architected materials have relied on advanced additive manufacturing techniques that are not yet scalable and yield small sample sizes. Additionally, most of these nano- and micro-architected materials have only been studied in the static regime, leaving the dynamic parameter space unexplored.

In this talk, we discuss advances in our understanding of architected materials by: (i) proposing numerical and theoretical tools that predict the behavior of architected materials with non-ideal geometries, (ii) presenting a pathway for scalable fabrication of tunable nano-architected materials, and (iii) exploring the response of nano- and micro-architected materials under three types of dynamic loading. We first explore the mechanics of lattice architectures with features at the micro- and millimeter scales, and discuss the effect of nodes (i.e., junctions) to obtain more accurate computational and theoretical predictive tools. Going beyond lattices, we propose alternative node-less geometries that exhibit extreme mechanical resilience at the nanoscale, and we harness self-assembly processes to demonstrate a pathway to fabricate them in cubic-centimeter volumes while maintaining nanoscale resolution. Lastly, we venture into the dynamic regime by designing, fabricating, and testing micro-architected materials that exhibit vibrational band gaps in the MHz regime as well as nano-architected materials with extreme energy absorption upon microparticle supersonic impact.

Abstract: Architected materials have been ubiquitous in nature, enabling unique properties that are unachievable by monolithic, homogeneous materials. Inspired by natural processes, man-made three-dimensional (3D) architected materials have been reported to enable novel mechanical properties such as high stiffness- to-density ratios or extreme resilience, increasingly so when nanoscale size effects are present. However, most architected materials have relied on advanced additive manufacturing techniques that are not yet scalable and yield small sample sizes. Additionally, most of these nano- and micro-architected materials have only been studied in the static regime, leaving the dynamic parameter space unexplored.

In this talk, we discuss advances in our understanding of architected materials by: (i) proposing numerical and theoretical tools that predict the behavior of architected materials with non-ideal geometries, (ii) presenting a pathway for scalable fabrication of tunable nano-architected materials, and (iii) exploring the response of nano- and micro-architected materials under three types of dynamic loading. We first explore the mechanics of lattice architectures with features at the micro- and millimeter scales, and discuss the effect of nodes (i.e., junctions) to obtain more accurate computational and theoretical predictive tools. Going beyond lattices, we propose alternative node-less geometries that exhibit extreme mechanical resilience at the nanoscale, and we harness self-assembly processes to demonstrate a pathway to fabricate them in cubic-centimeter volumes while maintaining nanoscale resolution. Lastly, we venture into the dynamic regime by designing, fabricating, and testing micro-architected materials that exhibit vibrational band gaps in the MHz regime as well as nano-architected materials with extreme energy absorption upon microparticle supersonic impact.

Abstract: Controlling elastic wave propagation and vibration has applications in many engineering disciplines, from protecting buildings from seismic waves to improving near-skull focused ultrasound in the brain. To expand this design space of achievable wave propagation and vibrational properties, research interest has grown in metamaterials, engineered structures that derive their large-scale effective properties from their small-scale repeated architecture. By appropriately designing the small repeated unit of a metamaterial, the overall properties of the system can be dramatically altered. For example, elastic metamaterials have been designed with negative effective stiffness or density, one-way elastic wave propagation, or elastic “black holes,” domains in which elastic waves are slowed down and cannot escape. This talk will describe the dynamics of several types of these metamaterial systems, from purely mechanical structures to more complex piezoelectric structures coupled to external circuitry. These systems exhibit a vibrational bandgap, or a frequency range over which waves cannot propagate through the structure. More interestingly, metamaterials with effective properties that vary in time and/or space enable wave propagation to be controlled with unprecedented precision, concentrating wave energy in prescribed areas or blocking waves only in certain directions. These novel capabilities will define the next generation of smart structures, incorporating smart materials, active control techniques, and fully programmable material properties into a single integrated system. Designing such complex systems requires collaboration across engineering disciplines, with numerous applications in aerospace structures, biological systems, and acoustics, among others.

Abstract: Continued advances in engineering technologies with increased complexity, enhanced performance and new capabilities, demand novel material systems with unprecedented properties as well as novel manufacturing approaches to accelerate the transfer of lab-scale inventions to the marketplace. Advanced materials, such as nanotubes and nanofilms, were demonstrated to be promising candidates for various applications including energy storage, electronics and transportation vehicles. Before advanced materials-based inventions can be widely applied to everyday life, their mechanical stability needs to be investigated, validated or engineered because it determines their long-term viability in all their applications. Also, by understanding the mechanical behaviors of advanced materials, novel material systems with tailored mechanical properties can be rationally designed for targeted applications. My central research interests and goals lie in experimentally investigating the length-scale dependent mechanical behaviors of advanced materials as well as applying the knowledge to develop advanced material systems tailored for specific applications, in particular, novel manufacturing technologies. In this talk, I will use graphene oxide as a representative material to showcase my journey of the experimental explorations of its multiscale mechanical behaviors from sub-nanometer scale to microscale as well as briefly showing some of my ongoing work on mechanics-guided design of novel material structures for the assembly of electronics and aerospace applications.

Abstract: Discrete dynamical systems resulting from classical mechanics or the spatial semi-discretization of the governing equations of continuum mechanics are described by systems of ordinary differential equations (ODEs) in time. These ODE systems are typically solved approximately at discrete time points using time integration algorithms. A unified theory was developed by Zhou, Tamma et al. to guide the design and analysis of such methods, obtaining a general computational framework which is applicable to linear and nonlinear 1st- and 2nd-order ODE systems. More recently, the framework was extended to systems of differential algebraic equations (DAEs) such as arising from subdomain decomposition. In this talk, I will summarize these prior developments in our research group and detail current efforts relating to the analysis of time integration algorithms, pairing of distinct methods in time and space for subdomain DAE problems, and the utility of reduced-order modeling for adaptive space-time refinement, with applications to solid/structural dynamics and coupled thermomechanical problems.

Abstract: The ultimate goal in manufacturing is the creation of a process that enables the economical and rapid fabrication of parts of arbitrary shape and material composition. This ideal, however, is often hindered by process constraints that significantly reduce the design space. More recently, Additive Manufacturing (AM) has evolved as a potent addition to conventional methods, promising almost unlimited design freedom and creating entirely new applications and fields. Despite the hype, however, AM has not yet prevailed in industry due to multiple major drawbacks. In my talk, I will demonstrate ways to partially overcome these drawbacks for both specific designs and the field as a whole.

In the first part, I will focus on the design of novel composite materials and structures with outstanding mechanical properties and new functionalities. I will further demonstrate AM-based solutions tailored to these specific designs that cannot be fabricated in any other way. The second part will address the general limitations of AM by providing detailed examples from recent research. Specifically, I will show how to overcome materials limitations, the resolution-scale trade-off, and the slow throughput speed. In both parts, computation plays a fundamental role. Finally, I will provide a perspective on the future direction of the field and outline possible next steps for my research.

Abstract: Additive manufacturing (AM) greatly expands the design freedom and near-net shape production of metallic components across multiple length scales. However, defects arising from starting materials, processing conditions, and post-processing may significantly affect the structural integrity and operational performance of metal AM parts. This paper seeks to elucidate common defects and defect formation mechanisms encountered in typical laser powder bed fusion (LPBF) AM processes. While the defect structures of conventional joining processes such as laser welding have been studied extensively, this talk primarily focuses on the nature of porosity transfer to the finished part exclusively for metal AM powder bed processing techniques. Multiple starting powders and analysis methods are summarized which demonstrate that the manifestation of defects within metal AM builds largely stems from the particular choice of process settings, with some influence of powder feedstock choice and post-processing heat treatments. Practical build strategies to limit the occurrence of defects by the use of process mapping and geometric modeling are also evaluated utilizing this fundamental understanding of defect formation. Such explorations may enable the validation and calibration of models to permit process qualification without the reliance on costly trial and error type experimentation currently employed.

Abstract: Given an inelastic material model, a structural geometry, and a set of boundary conditions, one can in principle always solve the governing equations to determine the system's mechanical response. However, for large inelastic systems this procedure can quickly become computationally overwhelming, especially in three-dimensions and when the material is locally complex, has microstructure.  In such settings multi-scale modeling offers a route to a more efficient model by holding out the promise of a framework with fewer degrees of freedom, which at the same time faithfully represents up to a certain scale the behavior of the system.

In this talk, we present a methodology that produces such models for inelastic systems upon the basis of a variational scheme.  The essence of the scheme is the construction of a variational statement for the strain energy as well as the dissipation potential for a coarse scale model in terms of the strain energy and dissipation functions of the fine scale model.  From the coarse scale energy and dissipation we can then generate coarse scale material models that are computationally far more efficient than either directly solving the fine scale model or by resorting to FE-squared type modeling. An essential feature for such schemes is the proper definition of the coarse scale inelastic variables.  By way of concrete examples, we illustrate the needed steps to generate successful models via application to finite deformation nonlinear viscoelasticity within the microsphere framework and by application to problems in classical plasticity.

Abstract: This talk investigates the motion of a liquid bubble trapped between an elastic sheet and a rigid substrate, with the goal of assessing the magnitude of the external force required to move the blister at constant velocity. The problem is formulated as a travelling-wave equation for the gap between the sheet and the substrate, together with a description of the boundary conditions at the propagating front-end and at the receding back-end contact line. The formulation accounts for the existence of a moving fluid front distinct from the separation edge. The configurational nature of the horizontal force acting at the back-end of the bubble is then discussed and expressions of this force are derived from variational and energy balance considerations.

Abstract: 2-dimensional (2-D) sharp interfaces with distinct boundaries demarcating an abrupt discontinuity in material properties in nanolayered composites have been studied for almost twenty years and are responsible for enhanced behaviors such as strength, radiation damage tolerance, and deformability. However, 2-D interfaces have their limitations with respect to deformability and toughness. 3-D interfaces are defined as heterophase interfaces that extend out of plane into the two crystals on either side and are chemically, crystallographically, and/or topologically divergent, in three dimensions, from both crystals they join. Here, we present the synthesis, structure, thermal stability, and mechanical behavior of nanolayered Cu/Nb containing interfaces with 3-D character. By co-sputtering the bimaterial interfaces between the constituent pure phases, the resulting compositional gradient gives rise to new interphase boundary structures. Micropillar compression results show that the strength of Cu/Nb nanocomposites containing 3D interfaces is significantly greater than those containing 2-D interfaces. Mechanical anisotropy, as well as shear banding is observed during pillar compression with retention of continuous layers across the shear band. We will present our recent results on deformation of such 3-D interfaces and structures, and describe their behavior mechanistically through the use of atomistic simulations.

Abstract: In the late 1980s, Sam Edwards proposed an equilibrium-like statistical mechanical framework to describe the properties of disordered granular materials. The key assumption underlying this theory was that all jammed packings are equally probable. A "granular entropy" was then defined as the logarithm of the number of such mechanically stable packings. Until recently it was not possible to compute granular entropies for systems larger than a couple of dozen particles, nor it was possible to test whether for a given protocol jammed packings are equiprobable as conjectured by Edwards. In this talk I will describe how granular entropies for much larger systems can now be computed using a novel algorithm. Then, I will discuss how both the extensivity of granular entropy and Edwards’ equiprobability hypothesis were tested by this method, in two and three dimensions. Finally, I will discuss future research directions, including first steps taken to implement the same approach to investigate the yielding transition in sheared amorphous solids.

References

[1] S. Martiniani, K. J. Schrenk, K. Ramola, B. Chakraborty, D. Frenkel, Numerical test of the Edwards conjecture shows that all packings become equally probable at jamming, Nature Physics 13, 848-851 (2017).

[2] S. Martiniani, K. J. Schrenk, J. D. Stevenson, D. J. Wales, D. Frenkel, Structural analysis of high dimensional basins of attraction, Physical Review E (Rapid Communication) 94, 031301 (2016).

[3] S. Martiniani, K. J. Schrenk, J. D. Stevenson, D. J. Wales, D. Frenkel, Turning intractable count- ing into sampling: computing the configurational entropy of three-dimensional jammed packings, Physical Review E 93, 012906 (2016).

Abstract:  By exerting mechanical forces, biological cells cause striking spatial patterns of localised deformation in the surrounding fibrous collagen matrix. Tether-like paths of high densification and fiber alignment form between cells, and radial hair-like bands emanate from cell clusters. While tethers may facilitate cell communication, the mechanism for their formation is unclear. In this study, modeling, numerical methods and computations are combined to show that tether formation is a densification phase transition of the fibrous extracellular matrix, caused by  microbuckling instability of network fibers under compression.  The mechanical behaviour of the extracellular  matrix (ECM) caused by cell contraction is modeled and analyzed from a macroscopic perspective employing the theory of nonlinear elasticity for phase transitions.   It is assumed that individual collagen fibers can sustain tension but buckle and collapse under   compression. Averaging over fiber orientations yields a two-phase bistable strain energy density   for fibrous collagen, with a densified second phase.   Simulated energy-minimizing deformations exhibit   strain discontinuities between the low- and the high-density phase, which localizes within intercellular  tethers and radial emanations from cell clusters, as experimentally observed. The formation of the localized deformations is due to the fact that the  resulting strain energy function  fails to be rank one convex, and essentially equivalent to a multi-well potential. This failure of rank-one convexity implies a  loss of ellipticity of the Euler-Lagrange PDEs of the corresponding energy functional.  For  a wide class of similar problems it is known that there exist oscillatory minimizing sequences with finer microstructures involving increasing numbers of  strain jumps. Similar behaviour is observed in computed solutions as the mesh size decreases. In order to show that this mesh dependence is not a numerical artefact,  a higher gradient term is added to the model. This term also introduces  an internal length scale, which is an additional material parameter related to characteristic fiber length, bending stiffness and other parameters of the fiber network.    To approximate  a variational problem involving a non rank-one convex strain-energy function, regularized by a higher gradient term, a non conforming finite element method is used.   It is shown that a suitable numerical scheme is utilized in the sense  that the numerical approximations indeed converge in the limit to  minimisers of the continuous problem.  This is done by employing the theory of Gamma-convergence  of the approximate energy minimization functionals to the continuous model when the discretization parameter tends to zero.  This is a rather involved task due to the structure of numerical approximations which are defined in spaces  with lower regularity than the space where  the minimisers of the continuous variational problem are sought.  Furthermore, when the energy functional contains terms with exponential growth, additional embedding theorems   are required.  For this purpose, an embedding  has been proved of piecewise polynomial spaces admitting discontinuities  in the gradient, into appropriate Orlicz spaces.   

Abstract: Interatomic potentials (IP) are widely used in computational materials science, in particular for simulations that are too computationally expensive for density functional theory (DFT). A large number of IP is available for a wide range of chemical elements and their mixtures. Most IP have a limited application range and often there is very limited information available regarding their performance for specific simulations. We performed extensive tests for the majority of the available potentials for unaries from the OpenKIM and NIST repositories as well as from other sources. The following properties types were considered: energy-volume curves, equilibrium bulk modulus, elastic constants, phonon spectrum and density of states, vacancy formation energies, transformation paths, surface energies, thermodynamic properties in the quasiharmonic approximation and thermal expansion. In addition, in order to access the transferability of IP we increase the coverage of atomic environments by considering a special set of random structures with one and two atoms in the unit cell and calculated its energetic, geometrical and elastic properties. Two typical cases of IP behavior - higher accuracy at the expense of lower transferability versus lower accuracy but higher transferability were identified. The results of our calculations are collected in a specially designed database for further analysis and will be available online.

Abstract: Dielectric elastomers (DEs) are a promising material for use in robotics, biomedical, energy, aerospace and automotive technologies. However, currently available DEs are limited by weak electromechanical coupling and our general understanding of DEs could improve. In this work, a multiscale model of dielectric elastomers is developed. At the molecular scale, an electrostatic response of a single DE monomer is assumed and, using statistical mechanics, the thermodynamics of a DE chain is investigated. This chain scale model leads to an important insight: the role of electrostatic torque on polymer chains in the electromechanical coupling of dielectric elastomers. This chain torque occurs because there is a connection between a chain's end-to-end vector and its polarization. At the continuum-scale, this macromolecular phenomenon manifests itself in the form of a deformation dependent susceptibility. Not only are novel modes of electromechanical coupling discovered, but also lessons learned from (standard) isotropic dielectric elastomers are then used to guide an in-depth analysis of the implications of designing and manufacturing anisotropic dielectric elastomers. The work in theoretical design reveals how the deformation and usable work derived from (anisotropic) dielectric elastomer actuators may be increased by as much as 75-100% relative to a standard, isotropic dielectric elastomer.

Abstract: Recently the Biot problem (1959), of surface instability in an elastic half space, has experienced renewed interest within the Mechanics community. Biot's original work applies the conventional methods of bifurcation theory to the problem of a three-dimensional half space composed of an incompressible Neo-Hookean material subjected to uniaxial far-field compressive stresses. Biot's results show that (a) the onset of instability occurs at an axial stretch of lambda = 0.544 where a structural bifurcation occurs; (b) the associated bifurcation modes correspond to sinusoidal surface waves (wrinkles) whose amplitude decays with distance below the surface of the half space; and (c) wrinkles of all wavelengths become unstable at the critical stretch (this is an example of failure of the "complementing condition" which is a necessary condition for stability of a boundary value problem with traction boundary conditions). More recently, experiments have shown that creases, consisting of spatially localized finite-strain deformations typically involving self-contact, are often observed well before the Biot critical value. Subsequently there has been a flurry of theoretical and numerical investigations aiming to explain the discrepancy between Biot's bifurcation results and the observation of creases. Based on these works, a portion of the Mechanics community has come to the conclusion that creases are a distinct "nonconventional" bifurcation phenomena (to be contrasted with "conventional" bifurcation phenomena characterized by a singularity of the energy's second Frechet derivative) that occur significantly before the Biot critical stretch. (This might be strictly correct for problems where continuity and differentiability are lacking, and thus the conventional methods of bifurcation theory are not complete or even applicable. Indeed, classical "first-gradient" elasticity theory, which is a good but not exact representation of physical reality, is one such non-smooth problem.) However, for (more physically realistic) models possessing sufficient continuity and differentiability properties, such as "second-gradient" elasticity theory, the Implicit Function Theorem guarantees that "creasing bifurcations," as envisioned in the recent literature, do not occur in any small neighborhood of the trivial family of homogeneous solutions.

In this work, we demonstrate numerically that, even in the first-gradient theory, creases (of nearly all spatial periodicities) occur naturally as the nonlinear evolution of "initially wrinkled" equilibrium paths. This is true for "primary bifurcations" that emerge from the uniformly strained equilibrium path, as well as for "secondary bifurcations" occurring along the primary bifurcation paths. In particular, we present results for an infinite two-dimensional plane-strain strip composed of a compressible Neo-Hookean material. In order to have a finite-dimensional primary bifurcation point (and eliminate the failure of the complementing condition) we consider two spatially inhomogeneous scenarios: (i) material stiffness that varies exponentially with distance from the surface, and (ii) a two-layer strip with a moderate stiffness contrast. Numerical computations of equilibrium paths are performed using the finite element method (FEM) with branch-following and bifurcation (BFB) methods to allow for the computation of stable and unstable segments of equilibrium paths. Self-contact effects are modeled using a simple plane-of-pure-repulsion potential energy term. Stability of equilibrium configurations is evaluated using the principle of minimum potential energy and Bloch wave theory. All simulation software was developed within the research group using the deal.ii FEM open-source library. Symmetry methods are used to eliminate the need for artificial imperfections and to carefully identify and characterize bifurcation points. Analytical results for the initial "wrinkled" post-bifurcation behavior and numerical results for the global evolution of "creased" equilibrium paths are presented and discussed.

Abstract: Achieving improved performance and efficiency of gas turbine engines implies higher material temperatures and more aggressive conditions along the hot gas path. Thermochemical interactions structural components and corrosive species in the combustion environment impact the (thermo-)mechanical performance of durability of these systems. This seminar will describe efforts to understand these coupled phenomena and develop materials solutions for two life-limited challenges. First, we will discuss the degradation of ceramic coatings induced by molten silicate deposits formed from ingested dust, sand, and volcanic ash. In this case, we have developed a coupled experimental/computational framework integrating computational thermodynamics modeling to predict the reaction products with thin-film mechanics models to predict crack driving forces and the likelihood of coating failure. We will then discuss the challenge of oxidative embrittlement of SiC-based ceramic matrix composites (CMCs) at intermediate temperatures. In this case, the effort seeks to understand how changes in the local chemical environment due to heterogeneity in the composite matrix microstructure influences the degradation of the mechanical properties of the reinforcing fibers. We will conclude with an outlook at opportunities to harness an understanding of high temperature materials phenomena to discover new materials and architectures.

Abstract: Recovery in crystalline materials is an energy-minimizing process of rearranging dislocation networks to form cells. These cells act as potential nuclei for spontaneous growth, also referred to as recrystallization, of defect-free grains. Subsequent evolution of defect-free grains is referred to as grain growth.

Recovery, recrystallization and grain growth are uniquely challenging phenomena to model since the ma- terials microstructure and deformation evolve at the same time scale. Grain boundary (GB) microstructure evolution in the absence of deformation is commonly modeled using phase field models, while the deforma- tion of a material with a fixed grain structure is modeled using crystal plasticity. In this talk, I will present a thermodynamically-consistent model we recently developed that describes bulk deformation and grain growth simultaneously. The model is rooted in the framework of polycrystal plasticity with grain boundaries described as geometrically-necessary-dislocations (GNDs). Moreover, the model’s energy functional is described on the entire five-dimensional grain boundary space allowing the consideration of both misorientation and inclination in the grain boundary energy. We demonstrate the richness of the model by simulating coupled grain boundary motion, grain rotation and shrinkage, dynamic recovery and anisotropic effects such as GB faceting.

Abstract: One fundamentally important aspect of learning models is the idea of learning a representation that has a few degrees of freedom, but that is still expressive enough to maintain accuracy. Traditionally, models are presented in the setting of discrete, structured grids, while they are naturally cast as questions of function approximation. 

Function approximations also suffer from the curse of dimensionality in applications that involve large-scale multiway arrays. Low-rank tensor decompositions have been successfully applied as a computational methodology for approximating and computing with these functions (Gorodetsky, and Jakeman [2018], Gorodetsky, et al., [2019]).

Here we present representation architectures that exploit the low-rank structure of multivariate objects (tensors and functions). These objects arise both as components of neural networks (e.g., weight matrices) or in more straight forward function approximation contexts. We briefly provide background on tensor representation, tensor decomposition, and Bayesian tensor decomposition approach. Finally, we present a continuous analogous of Bayesian low-rank decomposition, where the fully Bayesian model is efficient and provides uncertainty on the prediction results compared to the deterministic approach.

Abstract: The atomistic stress plays an important role in bridging atomic and continuum models of materials. The Hardy atomistic stress, which is defined as a weighted average over an averaging domain, is noisy at atomic length scales even for uniform loading conditions. This makes it difficult to obtain accurate stress estimates near atomic-scale defects such as nanocrack tips. In this work, we derive a rigorous stress-invariance condition for crystalline materials that leads to a class of lattice-dependent weighting functions defined in the reference configuration. This provides a smooth referential (Piola-Kirchhoff) stress field that is pushed forward to obtain the true (Cauchy) stress in the deformed configuration. The method is demonstrated by obtaining the stress field and stress concentration near the tip of a mode I nanocrack in silicon. The noise filtering algorithm is implemented in MDStressLab, a program to calculate atomistic stress fields available online at http://mdstresslab.org.

Abstract: One fundamentally important aspect of learning models is the idea of learning a representation that has a few degrees of freedom, but that is still expressive enough to maintain accuracy. Traditionally, models are presented in the setting of discrete, structured grids, while they are naturally cast as questions of function approximation. 

Function approximations also suffer from the curse of dimensionality in applications that involve large-scale multiway arrays. Low-rank tensor decompositions have been successfully applied as a computational methodology for approximating and computing with these functions (Gorodetsky, and Jakeman [2018], Gorodetsky, et al., [2019]).

Here we present representation architectures that exploit the low-rank structure of multivariate objects (tensors and functions). These objects arise both as components of neural networks (e.g., weight matrices) or in more straight forward function approximation contexts. We briefly provide background on tensor representation, tensor decomposition, and Bayesian tensor decomposition approach. Finally, we present a continuous analogous of Bayesian low-rank decomposition, where the fully Bayesian model is efficient and provides uncertainty on the prediction results compared to the deterministic approach.

Abstract: Flow diverter (FD) stents produced from thin film technologies based on shape memory alloys have a lot of unseen potential when compared to the commercially available counter parts. The ability to produce 3D structures on stent struts gives an additional edge to the design capabilities. The current project aims in developing new FD stents with increased functionality in the treatment of certain intracranial aneurysms, which are hard to treat with current FD stents. Finite Element Modeling is carried out in order to test the crimpability and Computational Fluid Dynamics for flow verification of stent designs, to find optimum designs.

Furthermore, validated stent designs are to be produced using thin film technologies and will be characterized for their functional behavior. The mechanical and structural functionalities are evaluated using various techniques to determine crimpability, radial force, flexural strength, wall opposition etc. The major part of the testing is flow characterization and this is to be carried out in co-operation with another project partner, where the produced stents will be tested for flow efficacy in 3D printed aneurysm models using MRI.

Abstract: We derive and analyze a novel approach for modeling and computing the mechanical relaxation of incommensurate 2D heterostructures.  Our approach parametrizes the relaxation pattern by the compact local configuration space rather than real space, thus bypassing the need for the standard supercell approximation and giving a true aperiodic atomistic configuration.  Our model extends the computationally accessible regime of weakly coupled bilayers with similar orientations or lattice spacing, for example materials with a small relative twist where the widely studied large-scale moire patterns arise.  Our model uses a generalized stacking fault energy for interlayer interactions and makes possible the simulation of the relaxation of multi-layer heterostructures for which a planar moire pattern does not exist.

Abstract: Cardiovascular soft tissues serve critical mechanical functions within the body, but pathologic changes to these tissues alter their material properties causing disruption or reduction in function. This loss can be sudden, such as the rupture of a myocardial infarct or aortic aneurysm; or it can be gradual, such as ventricular hypertrophy and heart failure or aneurysm dilation. Computational models have been employed to aid in the design of cardiovascular devices, but until recently, they have lacked predictive capacity. Predictions of long-term responses to interventions could only be assessed through expensive chronic animal and clinical trials and predictions of sudden failure events could only be achieved when a failure initiation region was pre-defined.

In this talk, I will share strategies for predicting the temporal and spatial characteristics of cardiovascular soft tissues. First, I will discuss my work on computational models to predict ventricular hypertrophy under overload conditions such as mitral regurgitation, aortic stenosis, and myocardial infarction. The results were fast, clinically applicable models of ventricular thickening and dilation. Second, I will discuss experimental testing and analysis techniques for determining the heterogeneous properties of soft tissues. I developed computational tools to identify regions with locally similar behavior within an intact whole tissue specimen as well as an inverse method that determines each region’s anisotropic, nonlinear material properties.

Abstract: The presence of interfaces can have a dramatic effect on phase behavior in materials. In this talk, I first describe a thermodynamic analysis of interfacial layering transitions at grain boundaries in binary alloys using both simplified lattice models and off-lattice semi-grand-canonical Monte Carlo simulations. In particular, diagrams are developed for these alloys that highlight the richness of the phase-like behavior of the system and, in particular, a series of first-order transitions and associated critical points. I will also describe the impact of these transitions on the mechanical and transport properties of polycrystalline solids, focusing on the Kapitza resistance of grain boundaries and the possibility of phonon engineering. Finally, I will examine the role of surface interactions on a simplified model of a biological system, namely immunoglobulin.

Abstract: Acousto-elastic metamaterials and phononic crystals are artificially architected materials endowed with the capability of mechanical wave manipulation. In recent years, endeavors have been made to achieve desired wave guiding properties in finite lattices by engaging edge states that are intrinsic to the unit cell topological invariants. The concept originates in the realm of quantum physics, in which in addition to their bulk bandgap behavior, topologically-protected edge states are created to progressively close the bandgap and enables edge wave propagation robust against a wide range of perturbations.

In the first part of my talk, a special class of topological phenomena occurring in Maxwell lattices will be introduced. Although the static behavior of ideal topological Maxwell lattices has been extensively studied theoretically, experimental proofs of the concept carried out on physical specimens that are realizable via simple fabrication techniques such as cutting, molding or printing have been rare. Via 3D scanning laser vibrometry characterization, we reveal how the zero-energy floppy edge modes predicted for ideal configurations morph into finite-frequency dynamic phonon modes that localize at edges of the physical lattice without the entanglement of low-frequency acoustic bulk modes. The experiments provide unequivocal evidence of the existence of strong asymmetric wave transport regimes at finite frequencies.

Next, I will discuss the design of elastodynamic logic circuits with unconventional wave transport capabilities at optical phonon modes comprising non-trivial waveguiding interfaces involving valley-Hall edge states that are robust against back-scattering at corners. We provide a rationale for the observed phenomena that blends topological considerations and mechanistic arguments, and we offer a criterion for the proper selection of the junction characteristics that are conducive to non-trivial interface modes. The arising experimental challenges associated with proper acquisition and deciphering of the in-plane modes are resolved via a systematic use of in-plane laser vibrometry.

Abstract: Mechanical metamaterials and phononic crystals are architected materials that owe their unique dynamic properties to an intelligent arrangement of their internal network of constitutive elements. These material systems display a variety of exotic wave manipulation properties, which include the formation of bandgaps, frequency-dependent wave anisotropy, waveguiding, anomalous refraction and cloaking. One of the main challenges in the design of metamaterial systems is endowing them with adaptive capabilities. A system is said to display adaptivity when it can spontaneously modify its response in reaction to sensed changes in the characteristics of the applied excitation. These properties grant the material the possibility to work far from their ideal design point. In the case of metamaterial architectures with multimodal and anisotropic phonons, adaptivity implies the ability to switch on and off certain modal or directional characteristics.

This work introduces a strategy for adaptivity that exploits the nonlinearity of the metamaterial as its main tuning mechanism. The idea is based on a new outlook on the well-known phenomenon of higher harmonic generation, which is revisited in the context of periodic structures with pronounced modal complexity. We show that, by playing with the amplitude of excitation, it is possible to switch on new features in the wave response, thus augmenting the modal and/or directivity landscape of the medium and overall enhancing its functionalities. The underlying mechanism is the tunneling of energy from a low-frequency acoustic mode to higher-frequency modes. The tunneling effects are especially interesting when the two modes linked by tunneling exhibit high complementarity, which can be quantified in terms of the degree of orthogonality between their mode shapes; in this scenario, the nonlinear functionality enrichment is maximized.

Through simulations, we will show several examples of inter-modal tunneling in material systems with different degrees of complexity, ranging from periodic waveguides with resonators to granular lattices. We will also provide experimental evidence of modal mixing phenomena observed in a compliant metamaterial prototype via 3D scanning laser vibrometry.

Abstract: Microstructure evolution features prominently in chemical reactions, phase transformations, and biological growth. In materials, this evolution is driven by electro-chemical, mechanical and thermal loads. The microstructure formed alters the physical properties of materials. I develop and apply mathematical models to investigate how microstructures evolve and how we can engineer these patterns to control material properties. In this talk, I will discuss phase field modeling of microstructures in two material systems: ferroelectrics and lithium battery electrodes. First, I will present how polarization patterns evolve in ferroelectric systems, and how these patterns can be applied to nanoscale actuators. Second, I will introduce my recent work on coupling lattice symmetry with the composition field, to describe phase transformation in lithium battery electrodes.

Abstract: It is widely acknowledged that no structures can be designed to be risk free, and therefore reliability analysis plays a central role in the design of engineering structures. The recent focus has been placed on structures made of brittle heterogenous (a.k.a. quasibrittle) materials, such as ceramics, composites, concrete, and many more at the microscale. We recently developed a level excursion model for analyzing the probabilistic failure of quasibrittle structures, in which the structural failure statistics is calculated as a first passage probability. The main feature of the model is that it captures both the spatial randomness of local material resistance and the random stress field induced by microstructures (e.g. randomly distributed flaws). It is shown that the model represents a continuum generalization of the classical weakest-link model, which recovers the Weibull distribution as an asymptotic distribution function. In this talk, I will discuss two applications of this model:
1) Modeling of strength distribution of polycrystalline silicon (poly-Si) MEMS structures based on 1D level excursion analysis. We show that the model agrees well with the experimentally measured strength distributions of poly-Si MEMS specimens of different sizes. The model predicts a complete size effect curve of the mean structural strength, which transitions from a vanishing size effect at the small-size limit to the classical Weibull size effect at the large-size limit.
2) Investigation of the tail distribution of strength of brittle and quasibrittle structures by extending the level excursion analysis to high dimensions. We show that the power-law tail distribution of structural strength stems from the tail distribution of material strength. Flaw statistics introduces additional randomness to the overall failure statistics of the structure, but does not dictate the power-law form of its tail distribution.

Abstract: Active textiles are an emerging area of research that could advance the capabilities of aerospace compression garment design by contracting on command. This research explores shape memory alloys (SMA), one class of smart materials that are characterized by thermomechanical or magnetomechanical coupling. Specifically, nickel titanium alloys (NiTi) are a common type of SMA that exhibit high recovery strains (~6-8%) and high recovery stresses (500-900 MPa) in response to changes in temperature, making them excellent thermomechanical actuators.  SMA knitted actuators are promising textile structures for aerospace garment applications due to their surface-wide distributed forces and deformation potential. This presentation provides an overview of prior work that has characterized the medical compression capabilities of SMA knitted actuators for on-body aerospace applications. The presentation explores the variables that determine the total system force capabilities, including (1) geometric design parameters, (2) macroscopic engineering strain, and (3) anthropometry.

Abstract: Semi-crystalline polymers, such as high density polyethylene (HDPE), are increasingly being used in infrastructure applications where they are exposed to corrosive environment that causes embrittlement of the initially highly deformable polymer. This study proposes a physically motivated damage constitutive model to predict the ductile as well as the brittle failures of HDPE based on its morphology. An elastic-viscoplastic model is used to capture the isochoric deformation mechanisms in the crystalline and amorphous phases. These deformation mechanisms cause network disentanglement and crystal breakdown, causing damage initiation in form of micro-voids in both the phases. Damage due to such homogeneous void growth causes a ductile failure of the polymer. However, the morphological changes due to chemical degradation enhances the localization of these voids into regions with well-defined planar boundaries, called crazes. The growth and breakdown of the crazes lead to formation of a traction free crack that causes brittle failure of the polymer. A continuum model is developed to incorporate the crazing mechanism of the rubbery amorphous phase of HDPE. The parameters of the model are calibrated using uniaxial tensile test at different strain rates, corrosion levels, and crystallinities. It is shown that the model can adequately capture the time-dependent stress-strain behavior over a large deformation and it can also predict the transition from ductile to brittle failure of HDPE in a corrosive environment.

Abstract: Real-time observations of mechanical and manufacturing processes provide valuable insights into the physics that governs the material behaviors involved. Thanks to the penetrating power of the high-intensity high-energy synchrotron X-rays, important sub-surface phenomena relevant to manufacturing and mechanics research can be captured with high spatial and temporal resolutions using high-speed synchrotron X-ray imaging. In this talk, I will elaborate on the development of synchrotron based high-speed X-ray imaging techniques to record the dynamics of additive manufacturing (AM) processes and fracture behaviors of AM materials. Specifically, I will present the observations of important physical phenomena that govern the laser powder bed fusion process, including dynamics of the melt pool and vapor depression, motion and spattering of the powders, and formation of porosity and structural defects. Further, I will briefly present the observations for binder jetting AM process, focusing on various mechanisms that can lead to defects in binder jetted parts. Along with the AM processes, I will also discuss my study on the deformation and fracture behaviors of AM materials under dynamic tensile loading conditions. The X-ray imaging experiments reveal that the unique microstructures formed during the AM build process largely influence the dynamic mechanical properties of these AM materials, in comparison to their cast counterparts. Finally, I will briefly discuss future research plans and avenues for collaboration.

Abstract: Advanced materials are internationally recognized as a foundation for new capabilities, tools, and technologies that meet urgent societal needs. “Advanced materials” broadly describes innovative materials that have atypical sizes, microstructures, and responses. These atypical characteristics enable major, previously impossible technological breakthroughs, yet many advanced materials owe their desirable properties to complex underlying micromechanics. Establishing the relationships between these local micromechanics and material performance is critical to the widespread implementation and evolution of advanced materials. Toward these goals, I utilize modern 3D X-ray diffraction techniques that offer the capability to measure the deformation and microstructure evolution inside bulk materials, in situ, and across nine orders of magnitude in length scales (nm to mm). Thus, these techniques can be used to simultaneously measure local microstructure events and the consequent macroscopic response. Guided by 3D X-ray diffraction experiments, I present several studies showing how material performance is dictated by local micromechanics and discuss the design approach of using “critical structure/microstructure features” to control micromechanics in ways that optimize material performance.

Abstract: High-energy X-ray experiments performed at synchrotron X-ray sources provide a unique means to probe the microstructure and micromechanical response of structural materials, including engineering alloys, during in-situ deformation. This talk will give an overview of how these new diffraction-based techniques can probe and reconstruct the deformation state of crystalline materials. Example applications of these techniques being used to study relevant materials problems including strain localization, deformation-driven phase transformations, and damage initiation will also be provided. In addition, the unique benefits of these measurements in comparison to traditional macroscopic mechanical testing will be highlighted with a detailed description of how far-field high-energy diffraction microscopy measurements, combined with finite element modeling, are used to deconvolve various crystallographic slip mechanisms in a hexagonal phase titanium alloy. This talk will conclude with a discussion of future avenues of technical development and scientific research regarding X-ray experiments, micromechanical constitutive modeling, and application to materials processing and design.

Abstract: Thanks to their advantageous strength/weight ratio, lattices structures are becoming more and more important in today's industrial designs. Their manufacturing has now become possible due to the development of new additive manufacturing processes. These materials are highly symmetric and, as a consequence, are prompt to fail with unstable behaviors when subjected to compression loadings. Predicting the onset of instability and the associated possible deformation modes is nowadays quite common but going further towards post-bifurcation can be challenging when considering such highly symmetric structures. Yet, when an instability occurs, it does not necessarily leads to catastrophic behaviors and the instabilities can even be taken advantage of to trigger new physical characteristics in the material. Methods to study the post-bifurcation behavior of such structures will be presented along with some recent results on important factors influencing the deformation modes.

Abstract: In bulk crystalline solids, the presence of compatible interfaces at microscopic scales is related to the lattice parameters describing the periodicity of their crystalline phases. Recent efforts in the tuning of such parameters to achieve compatibility of phases have led to remarkable macroscopic properties, including near-zero thermal hysteresis for such solids undergoing phase transformation. Can this line of thinking can be applied more generally? The structure of matter in many examples—in, for instance, nanoscience and biology—is that of discrete symmetries that are not inherently periodic: single wall carbon nanotubes of any chirality, BCN, GaN, MoS2, WS2, non-animal viruses such as the tail sheath of bacteriophage T4, bacterial flagella, and microtubules, to name a few. These are helical structures. In this talk, I will discuss phase transformations in helical structures and provide the  necessary and sufficient conditions on the structural parameters of the two helical phases such that they are compatible. These results provide a basis for the tuning of helical structural parameters so as to achieve compatibility of phases. Compatible helical transformations with low hysteresis and fatigue resistance would exhibit an unusual shape memory effect involving twist and possibly extension, and may have potential applications as new artificial muscles and actuators.

Abstract: One of the pervasive bottlenecks in science and engineering is the time-scale limitation of molecular dynamics (MD). Using accurate atomic forces, how do we perform an MD simulation on a large number of atoms for experimentally accessible time scales? In this work, we are developing the method of Objective Molecular Dynamics for this purpose. This is a method of simulation in which only a few (say 50-1000) atoms are actually simulated, but the full infinite set of atoms satisfy exactly the MD equations. We present a method, capable of simulating three parameter family of incompressible flows as well as compressible flow and unsteady flows. It allows us to calculate viscometric properties from a molecular-level simulation in the absence of constitutive equations, fluids in regime currently inaccessible to theory or experiment undergoing chemical reactions, high rates of shear, expansion or phase change which are far from equilibrium. We illustrate this method using Couette and Extensional flow. From a dynamical systems viewpoint, this is an (unstudied) invariant manifold of molecular dynamics. This invariant manifold provided by OMD is inherited by Boltzmann equation. We present fascinating connections with the Boltzmann equation and continuum mechanics.

Abstract: The discovery of new methods of generating energy without adversely affecting the environment is the most compelling scientific problem of our time. Due to continuously rising societal needs, energy is being both consumed and wasted in increasing quantities. Roughly 60% of unrecovered waste heat is considered ”low grade” because of the difficulty of converting small temperature differences to electric or mechanical energy using conventional technologies. Yet, the abundance of natural and industrial waste heat at small temperature differences is a growing and drastically underutilized stockpile of convertible energy. We present a novel energy conversion device that converts small temperature differences to electricity using ferroelectric capacitors. Ferroelectrics undergo a first-order phase transformation between a phase that is strongly polarized and a phase that is not polarized. We use analogies between the ferroelectric phase transformation and the first-order phase transformation utilized in steam engines to discuss thermodynamic efficiency and power density. We also demonstrate the conversion capabilities of such a device, present a theoretical framework to model the circuit parameters, and discuss using phase engineering to achieve extreme cyclic repeatability.

Abstract: In the design of engineering structures against extreme loading, such as explosions, impact, and blast, a key design parameter is the dynamic strength. The fracture strength of solids is known to depend on a range of factors such as the loading conditions, structure geometry, microstructural properties and inherent flaws. It has been shown that, at low strain rates, the failure of quasibrittle structures is featured by a damage localization mechanism. As a consequence, quasibrittle structures exhibit a size-dependent failure behavior, which transitions from quasi-plastic to perfectly brittle with an increasing structure size. Meanwhile, it is recognized that spatial fluctuations of microstructural properties could also lead to a size effect on the structural strength. Recent studies were able to capture the effect of this size-dependent failure behavior on the statistics of static strength, by a finite weakest link model. However, the weakest link model is a statistical representation of the damage localization mechanism, which has been shown to decrease with increasing loading rate. When subjected to dynamic loading, brittle and quasibrittle structures exhibit a strength enhancement and a diffused damage pattern with the initiation of many micro-fractures. This implies that the scaling behavior must vary with the applied strain rates, and the weakest-link model statistical representation of structural failure would need to gradually diminish in order to describe structural failure under dynamic loading conditions. This is achieved in the present study through the introduction of a rate-dependent length scale in the finite weakest link model, which captures the transition from localized to diffused damage with an increasing strain rate. The model’s predictions of the scaling behavior of the mean dynamic tensile strength and its standard deviation are in good agreement with the results of stochastic discrete element simulations of dynamic uniaxial tension of aluminum nitride specimens. The resulting probability distributions of the size and rate-dependent macroscopic tensile strength can be used as the input probability distributions in stochastic finite element simulations and help mitigate the mesh sensitivity of the output probability distributions of structural strength.

Abstract: Saccular intracranial aneurysms are a relatively common phenomenon in humans. Indeed, as much as 4% of the population develops such aneurysms in their lifetime. Most aneurysms are benign, but some will grow and rupture. When rupture does occur there is a high mortality rate.  Unfortunately, it is currently not possible to accurately predict which aneurysms are likely to rupture. Therefore, there is a need to develop improved modeling and simulation methodologies that are capable of identifying, in the early stages of aneurysm development, the characteristic signatures of aneurysms that will eventually rupture. In this work, we aim to model the mechanics of aneurysms as a tissue growth and remodeling process. Accordingly, we adopt a continuum kinematic-growth formulation for the tissue that postulates a multiplicative decomposition of the continuum deformation gradient into separate growth and elastic-deformation parts.  This is similar to many continuum models of plastic deformation.  Further, a separation of time-scales assumption is adopted such that elastic deformations may be treated as quasi-static relative to the time scale on which tissue growth evolves.  In this talk, we will first briefly review previous work on mixture theory growth models, and then we will describe the development of a custom finite element code (based on the deal.ii library) for simulating the dynamics of tissue growth in a symmetric hollow sphere subjected to controlled internal inflation.  Considering different mechanical loading rates, we aim to study the effect of tissue growth on the overall mechanical response of the sphere.  Some preliminarily results will be presented and discussed.

Abstract: Due to the extreme nonconvexity of the interatomic potential energy landscape the response of nanostructures to applied loading is inherently stochastic. This complexity is addressed head-on by the construction, using a branch-following and bifurcation approach, of an "Equilibrium Map" (EM) of the nanostructure. The EM describes all of the stable and unstable states of the structure and the transitions between them at each value of applied loading. A kinetic Monte Carlo (KMC) procedure with superbasin acceleration, adapted for time-dependent rate tables, is used to simulate the response of the nanostructure at arbitrary loading rates based on its EM. The method is applied to the uniaxial compression of a nanoslab of nickel modeled using a classical interatomic potential. The set of possible equilibrium solutions for this simple problem is surprisingly complex thereby demonstrating the need for such an approach.

Abstract: Magnesium (Mg) alloys, one of the most promising lightweight structural materials for automobile and aerospace applications, suffers from low strength and limited ductility at room temperature, due to a lack of available slip systems in hexagonal close-packed (hcp) structures. Improving strength without a concomitant loss of ductility is a hurdle to widespread application of Mg based materials. Rather than grain refinement or alloying with rare earth elements, our approach is to improve the strength and deformability of Mg alloys through stabilization of the bcc phase of Mg in metal laminates. Since bcc Mg can be stabilized when located between bcc Nb when the individual layer thickness is below 5 nm, the ductility is improved as bcc Mg has additional active room temperature slip systems over hcp Mg. In-situ TEM mechanical testing is a useful tool for real-time observation of deformation mechanisms at nanometer scales. Our results directly validate the hypothesis that bcc Mg can accommodate large plastic deformation and further reveal that in bcc/bcc Mg/Nb, a reversible bcc-hcp phase transformation occurs during loading and unloading. The fundamental understanding of deformation mechanisms of bcc Mg in Mg/Nb laminates are investigated utilizing a combination of experiments and modeling.

Abstract: Reciprocity or time reversal symmetry is a fundamental principle in wave propagation phenomena, which states that waves can symmetrically travel from one point to another in reversal manner. This is applicable in electromagnetic waves, optics, acoustic and mechanical waves. However, a growing area of interest is concerned with the breaking of the reciprocity principle for unidirectional elastic wave propagation, which can lead to the realization of acoustic systems analogous to electronic devices such as diodes. We have designed an acoustic diode and tested it experimentally. Geometric nonlinearities controlled by electromagnets are utilized at the unit cell level. Geometric nonlinearities allow the unit cell to change shape significantly while electromagnets allow dynamic tuning of the unit cell. This tuning allows for periodically modulating elastic properties of the structure in space and time. This spatiotemporal modulation of elastic modulus breaks mechanical reciprocity and induces one-way transmission of the waves, thus, enabling the structure to behave like an acoustic diode, which is analogous to an electronic diode.

Abstract: Plant materials exhibit a wide range of highly anisotropic mechanical behavior due to a hierarchy of micro-heterogeneous structures at different length scales. A rational understanding of mechanical behavior of plant materials will open the door for the biomechanical tailoring of plants for the specific bioengineering applications. we present a micromechanics approach that derives a hierarchical microstructure driven model of macroscopic stiffness and strength properties of anisotropic culm materials. As model input, it requires mechanical properties of the base constituents such as cellulose and lignin as well as morphology and volume fractions of all heterogeneous components at each hierarchical level. The latter can be retrieved from imaging data at different length scales, obtained from scanning electron microscopy, transmission electron microscopy and computed tomography (CT). Validating the predictions of macroscopic stiffness moduli and ultimate strength for bamboo material with measurements recently reported by Dixon and Gibson (J. Royal Soc. Interface, 2014), we demonstrate that the micromechanics model provides excellent accuracy without any further phenomenological calibration. In the next step, we plan to upscale the effect of microstructure instabilities on macroscopic material behavior. The goal of the work is to simulate the lodging behavior of oats to identify the significant traits in their genome to enable breeding of lodging resistant oats. Hence, in addition to the material model, an accurate and robust characterization of geometry from imaging datasets is an essential step. For the same, we developed a generic two-stage variational image segmentation model consisting of a flux augmented Chan-Vese energy functional for coarsely resolving local geometric features and phase field fractures inspired model to automatically eliminate the fine connections between the objects. We demonstrated the capability of our model in the context of bone segmentation. Our model is able to segment clinical CT datasets for femur and vertebra bones taken at the Academic Health Center of the University of Minnesota robustly and accurately.

Abstract: A consistent, small scale model of plastic motion in a crystalline solid is discussed which is based on a phase field description. By allowing for independent mass motion given by the phase field, and lattice distortion, the solid can remain in mechanical equilibrium on the timescale of plastic motion. Singular (incompatible) strains are determined by the phase field, to which regular distortions are added to satisfy mechanical equilibrium. A numerical implementation of the model is presented, and used to study a benchmark problem: the motion of an edge dislocation dipole in a two dimensional hexagonal lattice.

Abstract: Periodic architectured metamaterials are man-made heterogenous materials designed to have special properties, e.g. auxetic and fluid-like behavior. Currently, there is an interest in exploiting instabilities of such materials for certain applications (for example, buckling is used for energy trapping). It is believed that local parameters (within the periodic cell) control the onset of instabilities as well as the behavior of the material deep into the post-bifurcated regime.

The creation of a "unit cell design theory" for architecture materials will require developing an understanding of the relationships between local cell parameters, the onset of instability, and the post-bifucation behavior. In order to uncover such relationships and to accelerate the development of a unit cell theory, we revisit the classical problem of buckling of an axially loaded beam on an elastic foundation. We employ a set of analytical and numerical tools leading to bifurcation diagrams to explore the postbuckled regime of the system. Details of our computed bifurcation diagram are presented.  A systematic study of a previously unreported equilibrium solution branch and its associated bifurcation point is discussed.

Abstract: Additive manufacturing (a.k.a. 3D printing) is revolutionizing the manufacturing industry due to the significant advantages and capabilities, including rapid prototyping, fabrication of complex geometries, reduction of product development cycles, and high utilization of material. As metal AM becomes increasingly popular, a major barrier remains to rapidly qualify additive components that will meet functional requirement dictated by original design intent. Current methods to qualify AM parts heavily rely on experimental testing, which is very expensive and time consuming. The most obvious and promising approach to obtain rapid part qualification is through extensive use of computational modeling. This seminar will discuss the updated status of advanced modeling techniques at different scales in AM process. Also, current challenges and potential opportunities will be discussed to qualify AM components through a comprehensive simulation tool.

Abstract: With the broader objective of understanding the phenomenon of localization of deformation in nonlinearly elastic systems, the problem of stability of a classical Euler-Bernoulli beam on a nonlinear elastic foundation under axial compressive load is considered. In the first part of the talk, the initial post-critical behaviour of long length beams near the primary bifurcation point is discussed using a multi-scale perturbative expansion. Asymptotic analysis of the symmetric and the antisymmetric modes of deformation of the beam is presented for the limiting cases when the beam lengths become very large but stay finite.

In the second part, the global post-buckling regime of an infinitely long beam is investigated by applying a systematic numerical continuation method. Using a finite element discretization of the beam-foundation system subjected to appropriate periodic boundary conditions, a computational approach is discussed to calculate bifurcation paths leading to stable localized deformations. A parametric study is used to explore the effects of different nonlinear foundations (hardening, softening and restabilising). A representative sample of the resulting bifurcation diagrams and stability results are presented.

Abstract: In the case of shape memory alloys (SMAs), fundamental micromechanical theory has been an active area of research for more than 70 years. However, experiments to validate these theories on the microstructural scale are relatively new, challenging, and often limited to two-dimensional surface measurements. To address this open area, I utilize cutting-edge in situ synchrotron X-ray techniques such as near-field and far-field 3D X-Ray Diffraction (3DXRD) and Dark-Field X-Ray Microscopy (DFXM). Using these techniques, I present results from three particular experiments on NiTi SMAs: (1) A forward model algorithmic approach to indexing martensite in two-phase 3DXRD data is used to inform the use of martensite prediction criteria in modeling; (2) A full understanding of the relationships between microstructure evolution, deformation mechanisms, and macroscopic behavior is reported for reversible twin rearrangement (a.k.a. martensite reorientation); (3) The topology, misorientation, and elastic strains inside an austenite single crystal during thermally-induced transformation are shown with a spatial resolution of 100 nm. These three studies demonstrate how three-dimensional in situ diffraction techniques can be used to make huge leaps in our understanding of advanced materials and advanced deformation mechanisms.

Abstract: A methodology to build cross-linked atomistic structures for epoxy is presented. The methodology is based on a polymerization molecular dynamics (MD) scheme in which monomers are allowed to react with each other during an MD simulation. The criteria for forming chemical bonds is based on distances between prespecified reactive atoms on the monomers and growing polymer chains. A brief review of force fields (FFs) is also presented, the philosophy of various kinds of FFs is introduced, the advantage and disadvantage of several commonly used FFs are also discussed. As an example, the crosslinking process of DGEBA/D230 epoxy is simulated using the LAMMPS MD code with the Dreiding FF. The density, glass transition temperature (Tg), and Young's modulus of epoxy at different crosslinking conversion are calculated and compared with experimental data.

Abstract: Numerical branch following techniques are employed to efficiently determine solution paths of non-linear systems as a parameter is varied.  For equivariant equations, solution paths with nontrivial symmetry lie within an invariant subspace, called the fixed point space.  At symmetry-breaking bifurcation points, the Jacobian becomes singular.  Conveniently, this singularity is orthogonal to the fixed point subspace and one can construct the symmetry reduced problem on the fixed point space to solve a lower dimensional system of equations without singularity.  However, in practice the explicit construction of the reduced problem is computationally prohibitive for many problems of interest.  As an alternative, we are investigating algorithms that operate on the complete space but exploit symmetry information to improve their efficiency.  In this context, Krylov methods are attractive because they will naturally work within the fixed point space.  The robustness of such algorithms must be carefully considered because their numerical implementation (using floating-point math) may lead to departures from the fixed point space that could adversely affect convergence near singular points.  This work considers the implications of using Krylov-based solvers (e.g. GMRES) in the typical Newton-Raphson corrector step of branch following algorithms for symmetric systems.

Abstract: Rigid bars connected by elastic hinges are a popular model for demonstrating instabilities of planar elastic beams, such as elastic buckling (with one bar, one hinge and an axial load), or flutter instabilities (with two bars, two hinges and a follower force). By extending this planar set-up to three dimensions, we derive a discrete rod model. It is primarily defined in a discrete setting, which makes it appealing for simulations; it is also consistent with the classical theory of (continuous) beams when the length of the bars goes to zero. The 3d rotations of the directors, the bending and the twisting of the rod are represented based on ideas derived from discrete differential geometry. A detailed derivation of the model is proposed, the similarity and differences with the finite-element method are highlighted, and some applications to thin elastic rods and thin viscous threads are presented.

Abstract: Layered heterostructures formed by stacking two-dimensional (2D) materials are attracting considerable attention with remarkable properties. The registry-dependent nature of the van der Waals interactions between the layers can drive incommensurate to commensurate structural transitions complicating the mechanical and electronic behavior. We have developed a multiscale framework for simulating the mechanical response of 2D heterostructures. We use this method to study the structural relaxation in twisted graphene bilayers, which involves a localized rotation and shrinking of AA domains that scales in two regimes with the imposed twist. For small twisting angles, the localized rotation tends to a constant; for large twist, the rotation scales linearly with it. The results are validated experimentally through comparison to a simulated electron diffraction analysis of the relaxed structures. We predict a complex electron diffraction pattern involving the appearance of weak satellite peaks in the small twist regime. The mechanism of this new phenomenon is found to be intimately tied to the scaling behavior, and explained by using an analytical model in which the relaxation kinematics are described as an exponentially-decaying (Gaussian) rotation field centered on the AA domains. Both the angle-dependent scaling and diffraction patterns are in quantitative agreement with experimental observations.

Abstract: Recent advances in materials science enable the observation and control of microstructures such as line or point defects with remarkable precision. In this talk, I will discuss recent progress and open challenges in understanding how microscopic details in the kinetics of crystal surfaces can macroscopically influence the surface morphological evolution. In particular, the talk will explore via selected examples how the kinetics of microscale defects near surface plateaus, facets, can leave their imprints at larger scales.

Abstract: The talk will discuss various results (mostly drawn from joint work with R.D James) concerning compact sets of matrices that are compatible or incompatible for gradient Young measures, with connections to metastability in martensitic phase transformations.

Abstract: Soft robotics — an emerging field that seeks to create actuated systems using non-rigid materials — enables the design and characterization of broad new categories of physically-dynamic wearable systems. Traditional wearable robotic systems (e.g., rigid exoskeletons) primarily rely on hydraulic or servo-style actuators to create forces and displacements on the body; soft robotic systems eschew these rigid structures, offering similar functional benefits to the wearer in a superior, compliant, and often perceptually-invisible form factor. In this talk I will present work from the University of Minnesota's Wearable Technology Laboratory (WTL) investigating the use of soft robotic shape memory systems for on-body actuation. This talk will focus both on technology development (e.g., linear and two-dimensional actuation structures) and systems design for a variety of wearable technology applications (e.g., medical devices to improve lower body circulation, EVA/IVA systems for astronaut health and performance, behavioral interventions for autistic children, and shape-changing clothing for everyday consumer use).

Abstract: This talk will focus on an optimal design problem for multiphase composites. Mathematically, this optimal design problem is equivalent to the quasi-convexification of a multi-well energy function and is addressed by an indirect method. That is, a microstructure-independent bound is first derived for the effective energy function, and then, an optimal microstructure is explicitly constructed to attain this bound. Both directions can be quite non-trivial and are not fully solved for composites of three or more phases.

In the first part of the talk, I will present a new method of deriving the Hashin-Shtrikman bounds for multiphase composites which turn out to be the best known bounds. This method conveniently yields the optimality conditions for microstructures. Secondly, we show the optimality conditions cannot always be satisfied for composites of three or more phases. In particular, we find an explicit necessary and sufficient conditions for the optimality of the Hashin-Shtrikman bounds for three-phase isotropic conductive composites of isotropic materials. Finally, we present a necessary condition for smooth optimal microstructures and propose some open problems that may be of interest to analysts.

Abstract: We introduce a mesoscale model of a complex fluid to study the two phase interface separating a layered phase of uniaxial symmetry from an isotropic phase. The model is used to derive capillary and elastic contributions to local equilibrium conditions at deformed interfaces (generalized Gibbs-Thomson relations), extra stresses and their contribution to flow, and the nonequilibrium equations governing interfacial motion. Particular attention is paid to often neglected surface invariants such as the Gaussian curvature, and its role in driving changes of topology of the interface during its evolution. The methodology also lends itself to large scale computational analysis, with a parallel implemented pseudo-spectral approach. Focal conics are verified to be equilibrium shapes for the proposed phase field description. Our study is motivated by recent experiments on surface instabilities of toroidal focal conic domains in smectic films, and preliminary out of equilibrium results are shown to match some of the experimentally observed morphologies.

Abstract: Thin structures exhibit a broad range of mechanical responses as the competition between stretching and bending in these structures can result in buckling and localized deformations like folding and tension wrinkling. Active materials also exhibit a broad range of mechanical responses as features that manifest themselves at the microscale in these materials result in mechanical couplings at the engineering scale (thermal/electrical/dissipative) and novel function (e.g., the shape memory effect and piezoelectricity in select metal alloys and the immense fracture toughness of hydrogels). Given this richness in behaviors, my research broadly aims to address the following questions: What happens when active materials are incorporated into thin structures? Do phenomena inherent to these materials compete with or enhance those inherent to thin structures? Does this interplay result in entirely new and unexpected phenomena? And can all this be exploited to design new functions in engineering systems?

In this talk, we explore these questions in the context of a theoretical study of thin sheets of nematic liquid crystal elastomer. These materials are active rubbery solids made of cross-linked polymer chains that have liquid crystals either incorporated into the main chain or pendent from them. Their structure enables a coupling between the mechanical elasticity of the polymer network and the ordering of the liquid crystals, and this in turn results in fairly complex mechanical behavior including large spontaneous distortion due to temperature change, soft-elasticity and fine-scale microstructure.

We study thin sheets of nematic elastomer. First, we show that thin of sheets of a particular class of nematic elastomer can resist wrinkling when stretched. Second, we show that thin sheets of another class of nematic elastomer can be actuated into a multitude of complex shapes. In order to obtain these results, we systematically develop two dimensional theories for thin sheets starting from a well-accepted first principles theory for nematic elastomers. These characterize (i) the mechanical response due to instabilities such as structural wrinkling and fine-scale material microstructure, and (ii) thermal actuation of heterogeneously patterned sheets. For the latter, we show that the theory, which comes in the form of a two dimensional metric constraint, admits two broad classes of designable actuation in nonisometric origami and lifted surface. For the former, we show that taut and appreciably stressed sheets of nematic elastomer are capable of suppressing wrinkling by modifying the expected state of stress through the formation of microstructure. 

Abstract: Two-dimensional (2D) heterostructures created by stacking 2D materials are unique materials whose properties are controlled by the stacking order and orientation. To understand 2D heterostructures and accelerate the development of innovative nanotechnological devices based on these materials, molecular simulations with highly-accurate interatomic potentials are needed. Such potentials should not only provide an accurate description of the interactions within layers but also between layers as those play a vital role in defining the functionality of many 2D heterostructures. Using state-of-the-art data analytics, machine learning, and informatics, we are developing a fitting framework for automatically generating interatomic potentials for 2D heterostructures. In this talk I will discuss two potentials that have been developed: (1) a potential for molybdenum-disulfide based on a Fisher information theory analysis to gauge parameter sensitivity and model uncertainty; and (2) a bond-order interlayer potential for graphitic systems that accurately represents the energy and forces for stacking states that previous interlayer potentials cannot distinguish.

Abstract: Highly reversible phase transformation has been studied successfully using cofactor conditions (supercompatibility conditions between austenite and martensite phases). By forming perfect interfaces between austenite and martensitic microstructure, the reversibility is tremendously improved in different metallic alloy systems, reported by Eckhard Quandt (10 million tensile cycles of NiTiCuCo alloy) and Xian Chen (100,000 compressive cycles of AuCuZn). In this talk, I will discuss our recent results about how cofactor conditions play a role in reversibility for uniaxial tensile stress induced phase transformation for polycrystalline material. And in special cases, cubic to orthorhombic and cubic to monoclinic phase transformation, a further simplified form of cofactor conditions based on eigenvalues and eigenvectors of transformation stretch matrices is investigated. The simplified form provides a visual way to understand cofactor conditions.

Abstract: The lecture will summarize the most recent experimental and theoretical findings related to the topic of highly mobile interfaces, i.e. twin interfaces in shape memory alloys that are able to be set into motion under as small stresses as 0.01 MPa. It will be shown that these interfaces exhibit extremely complex morphologies involving many different scales of lamination, which opens new questions and new challenges for mathematical modelling. The current description of the highly mobile interfaces within the well-established mathematical theory of martensitic microstructures gives satisfying explanations of the experimentally observed morphologies, but does not provide any direct explanations of the high mobility itself. For this reason, kinematic multiscale models are nowadays developed, enlightening the relation between the morphology and the mobility. These models require deeper understanding of the mechanisms acting at all involved lengthscales, especially at the atomistic scale, where the formation of specific microstructures (modulations) is driven by quantum-mechanics effects.

Abstract: We present the micromagnetics of soft cubic ferromagnets with large magnetostriction, with the goal of understanding the single crystal Galfenol samples recently reported by Chopra and Wuttig. Taking first the no-exchange formulation of the micromagnetics energy, we construct minimizing sequences that yield local average magnetization and strain curves matching the experimental findings. Reintroducing then a sharp-interface version of the exchange energy, we pursue quantitative constructions to derive optimal energy scaling laws for the ansatz of normal and zig-zag Landau states; within the parameter regime of Galfenol, we show that the latter achieves lower energy scaling via equipartition of energy between the 90 degree wall energy, 180 degree wall energy, and the anisotropy energy. This forms the first step in adapting the program of Kohn and Müller to explain why certain magnetic microstructures are observed over others.

Abstract: Molecular simulations are the largest consumer of supercomputing time worldwide. Molecular simulations rely on one of the two models: accurate and very computationally expensive quantum-mechanical models, most notably the density functional theory, and empirical interatomic potentials that postulate a simple functional form of interatomic interaction that is fast to compute. Machine learning interatomic potentials (MLIPs) has recently been put forward as a promising methodology of combining the quantum-mechanical accuracy and the computational efficiency of the empirical potentials. MLIPs postulate a functional form that is fast to compute, yet flexible enough to be able to represent arbitrary interatomic interactions.

In my talk I will give an overview of the existing developments in the field of MLIPs, present the MLIPs developed in my group, and finally show how active learning can ensure reliability of such potentials. I will illustrate applications of such potentials in molecular dynamics, crystal structure prediction, prediction of alloy phase diagrams, and cheminformatics.

Abstract: The current trend of miniaturization in the electronics and the energy storage device industries has advanced research interests in material properties at the fine scale. Understanding the evolution of microstructures would provide insights on how to control and engineer nanoscale material properties. In this talk, I will provide an overview on the use of phase field models to investigate microstructural evolution in two material systems: ferroelectrics and lithium battery electrodes. First, I will present phase field modeling of electro-mechanically coupled systems and demonstrate the model's application to design nanoscale ferroelectric device concepts. Second, I will introduce my recent work on transformation based phase field crystal modeling approach, which couples lattice symmetry with phase composition. I explore an application of this model to describe phase transformation in lithium battery electrodes.

Abstract: Origami is an ancient art form about folding paper that originated in China, but was refined in Japan. From the point of view of solid mechanics, the deformation y: Omega -> R^3 from the reference sheet to the folded configuration, is a continuous isometric homotopy, which allows jumps of the deformation gradient at the fold lines. A helical Miura-ori (HMO) is an origami cylinder built by using an Abelian helical isometry group. An example is the Yoshimura pattern. We give a general method of constructing HMO structures, and we comment on their rigidity. Inspired by the theory of phase transformations in helical structures that we have developed, we construct compatible interfaces between two phases of an HMO. By transforming one phase to the other, and despite the generic rigidity, we can approximate deformable helical Miura-ori.

Abstract: Continuum hypothesis based properties, for example, elastic modulli or thermal conductivity of a material at small lengths scale can be derived efficiently using molecular mechanics or dynamics. While doing so one makes a few key assumptions and develops what are called as equivalent continuum structures (ECSs). Accuracy of the derived quantity for a given structure thus depends strongly on its ECS. In this talk we will first present development of ECSs for single-walled carbon nanotubes (SWCNTs) and graphene based on the theory of linear vibrations and show instances when these ECSs may fail or behave counterintuitively. Subsequently, results from two methods leading to conflicting values of critical buckling strain in SWCNTs under compression will be presented. Lastly, we will present some very recent results on instabilities in carbon nanocone stacks.

Abstract: Using the framework of the Ball-James model we propose a new theory to predict features of the (557) and (111) lath transformation observed in low-carbon steels. Our approach generates a one-parameter family of possible habit plane normals and a selection mechanism then identifies the (557) and (111) normals as those arising from a deformation with small atomic movement and maximal compatibility. Compared to existing theories which require 7 or more fitted parameters our theory only uses the assumption of energy minimisation and compatibility. Interestingly, the theory predicts that a type of twinning mechanism is involved - instead of the commonly proposed high dislocation density.

Abstract: Experimental studies on single molecules of DNA have reported a rich variety of structural transitions, including coexistence of three phases, in a torsionally constrained molecule. A comprehensive knowledge of these structural transitions is useful for unraveling the in vivo and in vitro behavior of DNA. Our objective is to understand the structural transitions in a torsionally constrained DNA molecule when it is pulled using optical or magnetic tweezers. We use foundational concepts from the Zimm-Bragg helix-coil transition theory and merge them with ideas from the theory of fluctuating elastic rods to model the mechanics of DNA. We also account for the electrostatic interactions between the ions and the negatively charged phosphate backbone of DNA. Using our model we calculate the force and torque corresponding to the over-stretching transition characterized by a 70% jump in the contour length of the molecule and examine the effect of salt concentration on this transition. We also deduce conditions under which the co-existence of B-, S- and P-DNA is possible. We examine how the cooperativity parameter for each transition affects the force-extension curve or torque-rotation curve. We attempt to rationalize the non-monotonic dependence of external work done on the ion concentration by connecting it to the electrostatic dependence of the interfacial energy between two phases of DNA. As a second topic we will consider thermal fluctuations of lipid bilayer membranes. Typically, membrane fluctuations are analyzed by decomposing into normal modes or by molecular simulations. We propose a new approach to calculate the partition function of a membrane. We view the membrane as a fluctuating elastic plate and discretize it into triangular elements. We express its energy as a function of nodal displacements, and then compute the partition function and covariance matrix using Gaussian integrals. We recover well-known results for the dependence of the projected area of the membrane on the applied tension and recent simulation results on the dependence of membrane free energy on geometry, spontaneous curvature and tension. As new applications we compute elastic and entropic interactions of inclusions in membranes.

Abstract: The dynamic fracture of brittle solids is a particularly interesting collective interaction connecting both large and small length scales. Apply enough stress or strain to a sample of brittle material and one eventually snaps bonds at the atomistic scale leading to fracture of the macroscopic specimen. We discuss a nonlocal mesoscopic model for calculating dynamic fracture. The force interaction is derived from a double well strain energy density function, resulting in a non-monotonic material model. The material properties change in response to evolving internal forces eliminating the need for a separate phase field to model the fracture set. The model can be viewed as a regularized fracture model. In the limit of zero nonlocal interaction, the model recovers a sharp interface evolution characterized by the classic Griffith free energy of brittle fracture with elastic deformation satisfying the linear elastic wave equation off the crack set. We conclude with a brief numerical analysis of the model which is joint work with Prashant Jah.

Abstract: The response of the muscle-tissue unit (MTU) to activation and applied forces is affected by the architectural details as well as the material properties of this nearly-incompressible tissue. We will describe the (highly nonlinear) elastic equations governing this response for a fully three-dimensional, quasi-static, fully nonlinear and anisotropic MTU. We describe a three-field formulation for this problem, and present a DG discretization strategy. The scheme was implemented using {\tt deal.ii}. We present computational results about the effects of localized activation as well as the effects of fatty tissue on muscle response. This is joint with Sebastian Dominguez, Hadi Rahemi, David Ryan and James Wakeling.

Abstract: In this work, we present our continuum limit calculations of electrical interactions in ionic crystals and dielectrics. Continuum limit calculations serve two main purposes. First, they give an idea of how the macroscopic behavior of the material is related to the interactions at the atomistic scale. Second, they help in developing a multiscale numerical method, where the goal is to model the material both at the scale of atoms and at the macroscale. We consider two important settings: nanorod-like materials, where the thickness of a material in the lateral direction is of the order of the atomic spacing, and the materials, where atoms are randomly fluctuating due to the thermal energy. Our calculations, for the nanorod-like materials, show that the electrostatics energy is not long-range in continuum limit. We also consider the discrete system of dipole moments along the straight line and along the helix. We then compute the limit of the energy as the separation between the dipole moments tends to zero. The energy, in the continuum limit, is short-range in nature. This agrees with the calculations of Gioia and James for the magnetic thin films. We consider the system of atoms which are fluctuating due to thermal energy. We model the charge density field as a random field and compute the continuum limit of the electrostatics energy.

Abstract: The occurrence of generic degeneracies in physical systems is closely related to underlying symmetries of the governing equations. The occurrence of additional non-generic degeneracies which cannot be accounted for by usual symmetry arguments is usually termed as accidental. In this work, we formulate a mechanistic framework which helps identify and investigate a particular class of degeneracies associated with equivariant systems under certain common symmetry groups. We show that the existence of a first-integral for such systems (i.e., a potential function or energy functional) along with certain mathematical properties of such symmetry groups guarantees generically that non-generic degeneracies in the spectrum of the Jacobian of the governing equations (and likely other properties of the system) occurs. We apply our theory to three common physical systems and show that it successfully explains the "accidental" degeneracy found in (1) the stiffness matrix associated with truss structures having cyclic symmetry, (2) electronic properties of periodic, cyclic and helical structures without inversion symmetry, and (3) the elastic constants matrix in the theory of linear elasticity.