Periodic homogenization of Prandtl-Reuss plasticity equations in arbitrary dimension
Ben Schweizer, Marco Veneroni · Technische Universität Dortmund Eldorado (Technische Universität Dortmund) · 2010
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 n > 0. We study the limit n -> 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.