Research Topic

Topic: Cascading CauchyBorn FEM
Team: Ryan Elliott, Ellad Tadmor
Collaboration:
Third Wave Systems, Inc.
Funding: MnDRIVE, University of Minnesota
Figure:
A CCB FEM simulation of a shapememory cycle. The colors correspond to inplane shear highlighting the phase transformations occurring in the material. In the top row, an austenite specimen is initially cooled to create a random microstructure of martensite. It is then sheared, which causes phase transformations to align the martensitic variants. In the second row, the specimen is heated above its transformation temperature and recovers the original austenite phase returning to its original shape. Thus the material exhibits "memory". Figure taken from Sorkin et al. (2014) (see below).

Description:
The quasicontinuum (QC) method, in its local (continuum) limit, is applied to materials with a multilattice crystal structure. CauchyBorn (CB) kinematics, which accounts for the shifts of the crystal motif, is used to relate atomic motions to continuum deformation gradients. This method can be used to study phase transformations as happens for example in diamond anvil cell experiments. To avoid failures of CB kinematics, QC can be augmented with a phonon stability analysis that detects lattice period extensions and identifies the minimum required periodic cell size. This approach is referred to as Cascading CauchyBorn kinematics (CCB). The result is a finite deformation (nonlinear) finite element formulation that uses an atomistbased constitutive relation capable of modeling phase transformations.
Publications:

"A Local Quasicontinuum Method for 3D Multilattice Crystalline Materials: Application to ShapeMemory Alloys",
V. Sorkin, R. S. Elliott and E. B. Tadmor,
Modelling and Simulations in Materials Science and Engineering, 22, 055001 (2014).
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"Efficient Algorithms for Discrete Lattice Calculations",
M. Arndt, V. Sorkin and E. B. Tadmor,
Journal of Computational Physics, 228, 4858–4880 (2009).
pdf  doi  bibtex

"A Multilatice Quasicontinuum for Phase Transforming Materials: Cascading CauchyBorn Kinematics",
M. Dobson, R. S. Elliott, M. Luskin and E. B. Tadmor,
Journal of ComputerAided Materials Design, 14, 219–237 (2007).
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"Polarization Switching in PbTiO_{3}: An ab initio Finite Element Simulation",
E. B. Tadmor, U. V. Waghmare, G. S. Smith and E. Kaxiras,
Acta Materialia, 50, 2989–3002 (2002).
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"Multiscale Simulations of Silicon Nanoindentation",
G. S. Smith, E. B. Tadmor, N. Bernstein and E. Kaxiras,
Acta Materialia, 49, 4089–4101 (2001).
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"Multiscale Simulation of Loading and Electrical Resistance in Silicon Nanoindentation",
G. S. Smith, E. B. Tadmor and E. Kaxiras,
Physical Review Letters, 84, 1260–1263 (2000).
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"Mixed Finite Element and Atomistic Formulation for Complex Crystals",
E. B. Tadmor, G. S. Smith, N. Bernstein and E. Kaxiras,
Physical Revew B, 59, 235–245 (1999).
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