Volume 24, Number 1, January-March 2018
|Page(s)||153 - 176|
|Published online||17 January 2018|
Stochastic homogenization of plasticity equations
1 Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin, Germany.
2 TU Dortmund, Fakultät für Mathematik, Vogelpothsweg 87, 44227 Dortmund, Germany.
Received: 27 April 2016
Accepted: 31 January 2017
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 ε > 0 denotes the typical length scale of oscillations. We derive effective equations that describe the behavior of solutions in the limit ε → 0. The homogenization procedure is based on the fact that stochastic coefficients “allow averaging”: For one representative volume element, a strain evolution induces a stress evolution . Once the hysteretic evolution law Σ is justified for averages, we obtain that the macroscopic limit equation is given by −∇·Σ(∇su) = f.
Mathematics Subject Classification: 74C05 / 35R60 / 74Q10
Key words: Small strain plasticity / stochastic homogenization
© EDP Sciences, SMAI 2018
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.