PERIODIC HOMOGENIZATION OF THE PRANDTL–REUSS MODEL WITH HARDENING

Abstract

We study the n-dimensional wave equation with an elastoplastic nonlinear stress–strain relation. We investigate the case of heterogeneous materials, i.e., x-dependent parameters that are periodic at the scale η>0. We study the limit η→0 and derive the plasticity equations for the homogenized material. We prove the well-posedness for the original and the effective system with a finite-element approximation. The approximate solutions are also used in the homogenization proof which is based on oscillating test functions and an adapted version of the div-curl Lemma.