Mathematical homogenization of nonperiodic heterogeneous media subjected to large deformation transient loading

We present a generalization of the classical mathematical homogenization theory aimed at accounting for finite unit cell distortions, which gives rise to a nonperiodic asymptotic expansion. We introduce an auxiliary macro‐deformed configuration, where the overall Cauchy stress is defined, and nonperiodic boundary conditions. Verification studies against a direct numerical simulation demonstrate the versatility of the proposed method.