Stress average rule derived through the principle of virtual power

Abstract Stress and strain average rules are the key conceptual pillars of wide field continuum micromechanics materials. The aforementioned express that spatial (micro‐)stress (micro‐)strain fields throughout a microscopically finite representative volume element (RVE) equal to (macro‐)stress (macro‐)strain values associated with corresponding macroscopically infinitesimal (macroscopic material point). According famous contribution Hashin, stress derived from equilibrium compatibility conditions, together (micro‐)displacement (micro‐)traction boundary conditions homogeneous (macro‐)strains (macro‐)stresses, respectively. However, as, strictly speaking, only displacements or tractions can be described at boundary, remaining rule turns out as mere definition. We here suggest way do without such definition, by resorting principle virtual power (PVP) means guarantee mechanical equilibrium: RVE, we prescribe (micro‐)velocities, which linked arbitrary, but (macro‐)velocities rates, while latter also linked, in multilinear fashion, microscopic rate inside RVE. Considering, under these equivalence macroscopic expressions for densities internal external forces yields well‐known and, case uniform force fields, rule. same strategy applied an RVE hosting single between atomistic mass points, readily “internal virial tensor.”