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 solids. Our formulation is then validated by considering both a homogeneously strained crystalline solid and one containing an oversized inclusion. In the latter case a direct comparison is made with results from anisotropic elasticity theory. We find that we are able to obtain good agreement with the suitably averaged continuum solutions in the far-field regime. Moreover, the coarse-grained tensor derived here appears to offer superior accuracy as compared to a stress tensor that has been widely used in atomistic analysis.