WIAS Preprint No. 2258, (2016)

Stochastic homogenization of rate-independent systems



Authors

  • Heida, Martin

2010 Mathematics Subject Classification

  • 74QXX 74C05 34E13

Keywords

  • Rate-independent, stochastic homogenization, convex functionals, two-scale

Abstract

We study the stochastic and periodic homogenization 1-homogeneous convex functionals. We proof some convergence results with respect to stochastic two-scale convergence, which are related to classical Gamma-convergence results. The main result is a general liminf-estimate for a sequence of 1-homogeneous functionals and a two-scale stability result for sequences of convex sets. We apply our results to the homogenization of rateindependent systems with 1-homogeneous dissipation potentials and quadratic energies. In these applications, both the energy and the dissipation potential have an underlying stochastic microscopic structure. We study the particular homogenization problems of Prandlt-Reuss plasticity, Coulomb friction on a macroscopic surface and Coulomb friction on microscopic fissure.

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