Stochastic homogenization of plasticity equations

2016/04/08 by Heida, M., Schweizer, B. · 1 citation
#74C05 #74Q15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.02291

Abstract

In the context of infinitesimal strain plasticity with hardening, we derive a stochastic homogenization result. We assume that the coefficients of the equation are random functions: elasticity tensor, hardening parameter and flow-rule function are given through a dynamical system on a probability space. A parameter \eps>0 denotes the typical length scale of oscillations. We derive effective equations that describe the behavior of solutions in the limit \eps→ 0. The homogenization limit is based on the needle-problem approach: We verify that the stochastic coefficients "allow averaging": In average, a strain evolution [0,T]\ni t↦ ξ(t) ∈ \symM induces a stress evolution [0,T]\ni t↦ Σ(ξ)(t) ∈ \symM. With the abstract result of [9] we obtain the stochastic homogenization limit.

Cited by

• Homogenization of elasto-plastic plate equations with vanishing hardening

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