A mathematical homogenization perspective of virial stress

A continuum stress measure is derived from molecular dynamics equations using a generalized mathematical homogenization (GMH) theory. GMH consists of solving a coupled fine-scale (atomistic unit cell) problem and a coarse-scale (continuum) problem. The fine-scale problem derived can be interpreted as a molecular statics (at 0 K) problem, where the coarse-scale problem derived is a constitutive law-free continuum equation, which calculates the Cauchy stress directly from atomistics. The continuum stress derived is compared to various versions of the virial stress formula