Stochastic homogenization on perforated domains II – Application to nonlinear elasticity models

Abstract

AbstractBased on a recent work that exposed the lack of uniformly bounded extension operators on randomly perforated domains, we study stochastic homogenization of nonlinear p‐elasticity, , on such structures using instead the extension operators constructed in former works. We thereby introduce two‐scale convergence methods on such random domains under the intrinsic loss of regularity and prove some generally useful calculus theorems on the probability space, for example, abstract Gauss theorems.