Stress calculation in atomistic simulations of perfect and imperfect solids

We analyze a real-space expression for the local stress tensor. This tensor rigorously satisfies conservation of linear momentum. From this expression a coarse-grained tensor is obtained for use in atomistic simulations of so lids. Our formulation is then validated by considering both a homogeneously strained crystalline solid and one containing an oversized inclusion. In t he latter case a direct comparison is made with results from anisotropic el asticity theory. We find that we are able to obtain good agreement with the suitably averaged continuum solutions in the far-field regime. Moreover, t he coarse-grained tensor derived here appears to offer superior accuracy as compared to a stress tensor that has been widely used in atomistic analysi s. (C) 2001 American Institute of Physics.