Research Topic

[Atomistic Stress] Topic: Atomistic Definitions of Stress

Team: Min Shi, Nikhil Admal, Ellad Tadmor

Collaboration: Nikhil Admal (U. Illinois Urbana-Champaign)

Funding: None.

Figure: The stress distribution around a hole in a nanoscale plate consisting of about 180,000 atoms (shown as dots) interacting via a Lennard Jones potential.

Description: At the molecular level there are atoms and forces, whereas continuum theories deal with fields and stress. To connect between these models of reality it is necessary to obtain expressions for continuum variables, such as stress and heat flux, at the molecular level. To date, many different expressions have been proposed and some confusion exists in the literature as to which is "correct". In this project, we showed that a unified framework, based on the work of Irving and Kirkwood (IK) and later Noll, can be established from which all other expressions can be derived. Further this framework is applicable to arbitrary interatomic potentials, and therefore extends the IK derivation which was limited to pair potentials. Interestingly, it turns out that subtle arguments related to the nature of interatomic potentials play an important role in the derivation and lead to the conclusion that the atomistic stress tensor is nonunique in a previously unrecognized manner. This formulation leads to practical algorithms to filter out noise from stress fields. In addition, the nonuniqueness of the stress tensor can be addressed within a variational framework.

Open source software (MDStressLab) based on this research for computing stress fields from molecular dynamics simulations (and their decomposition into unique and non-unique parts) is available at