Evaluation of continuum stress in atomistic simulation

Abstract

One of the key issues of multiscale and mechanical modeling is related to the developing definitions for continuum variables that are calculable within an atomic system. The instantaneous atomic contributions to these averages do not have the same physical interpretation as the corresponding “point-wise” continuum quantities. A classic example is the Cauchy or true stress and the ensemble stress defined by the virial theorem (VT). The chapter compares stress for atomistic systems as described by the virial theorem to obtain results using an expression for the Cauchy stress derived by R.J. Hardy. As a function of increasing cutoff radius for the stress analysis volume, the Hardy description of stress displays a convergence to values expected from continuum theory than volume averages of the local virial stress. Furthermore, the behavior of Hardy's expression near a free surface is consistent with the mechanical definition for stress. The analysis has shown that the definition for Cauchy stress in an atomic system developed by Hardy does a better job than the expression based on the virial theorem. The results also indicate that the fluctuations in stress for systems at finite temperature are larger in magnitude than at zero temperature.