Stochastic homogenization of rate-independent systems
- Heida, Martin
2010 Mathematics Subject Classification
- 74QXX 74C05 34E13
- Rate-independent, stochastic homogenization, convex functionals, two-scale
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.
- Contin. Mech. Thermodyn., 29 (2017), pp. 853--894, DOI 10.1007/s00161-017-0564-z .