Repository: Freie Universität Berlin, Math Department

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

Heida, M. and Nesenenko, S. (2017) Stochastic homogenization of rate-dependent models of monotone type in plasticity. SFB 1114 Preprint in arXiv:1701.03505 . pp. 1-26. (Unpublished)

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Official URL: https://arxiv.org/abs/1701.03505

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 Γ-convergence theory.

Item Type:Article
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
ID Code:2213
Deposited By: Silvia Hoemke
Deposited On:15 Feb 2018 16:10
Last Modified:15 Feb 2018 16:13

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