Periodic homogenization of Prandtl-Reuss plasticity equations in arbitrary dimension
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Date
2010-03-12T11:11:14Z
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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 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.
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Keywords
homogenization, plasticity, two-scale model, differential inclusion, nonlinear wave equation