WIAS Preprint No. 2366, (2017)

Stochastic homogenization of rate-dependent models of monotone type in plasticity



Authors

  • Heida, Martin
  • Nesenenko, Sergiy

2010 Mathematics Subject Classification

  • 74Q15 74C05 74C10 74D10 35J25 34G20 34G25 47H04 47H05

Keywords

  • Stochastic homogenization, random measures, plasticity, stochastic two-scale convergence, Gamma-convergence, monotone operator method, Fitzpatrick's function, Palm measures, random microstructure

DOI

10.20347/WIAS.PREPRINT.2366

Abstract

In this work we deal with the stochastic homogenization of the initial boundary value problems of monotone type. The models of monotone type under consideration describe the deformation behaviour of inelastic materials with a microstructure which can be characterised by random measures. Based on the Fitzpatrick function concept we reduce the study of the asymptotic behaviour of monotone operators associated with our models to the problem of the stochastic homogenization of convex functionals within an ergodic and stationary setting. The concept of Fitzpatrick's function helps us to introduce and show the existence of the weak solutions for rate-dependent systems. The derivations of the homogenization results presented in this work are based on the stochastic two-scale convergence in Sobolev spaces. For completeness, we also present some two-scale homogenization results for convex functionals, which are related to the classical Gamma-convergence theory.

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