Periodic homogenization of Prandtl-Reuss plasticity equations in arbitrary dimension

Abstract

We study the n-dimensional wave equation with an elasto-plastic 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 used in the homogenization proof which is based on oscillating test function and an adapted version of the div-curl Lemma. MSC: 74Q10, 35L70, 74D10.