Interatomic potential energy representation and the atomistic stress tensor
Nikhil Chandra Admal (University of Minnesota), Ellad Tadmor (University of Minnesota)
From Atomistics to Reality: Spanning Scales in Simulations and Experiments Symposium A
Wed 1:30 - 2:50
CIT 165
Recent advances in multiscale methods have renewed our interest in the interpretation of continuum fields for atomistic systems. In particular, the atomistic stress tensor has been studied extensively due to its non-uniqueness, mostly within the context of spatial averaging [1]. In this talk, we identify a new source of non-uniqueness which is related to the representation of the interatomic potential energy [2]. Interestingly, it turns out that subtle arguments related to the nature of interatomic potentials play an important role in determining the nature of the force decomposition, which in turn is related to the non-uniqueness and symmetry of the stress tensor. Moreover, this non-uniqueness becomes practically relevant in the context of interatomic potentials which are not expressed as a function of distances or angles, for example the GAP potential. We characterize the non-uniqueness of the stress tensor in this context, and present a differential-geometric viewpoint. This leads to a unique stress tensor irrespective of the choice of potential energy representation. Various numerical experiments are conducted to compare the new definition with existing ones. References [1] A. I. Murdoch. A critique of atomistic definitions of the stress tensor. Journal of Elasticity, 88:113-140, 2007. [2] N. C. Admal and E. B. Tadmor. A unified interpretation of stress in molecular systems. Journal of Elasticity, 100:63-143, 2010.