Stochastic Unfolding and Homogenization of Spring Network Models

Abstract

The aim of our work is to provide a simple homogenization and discrete-to-continuum procedure for energy driven problems involving stochastic rapidly-oscillating coefficients. Our intention is to extend the periodic unfolding method to the stochastic setting. Specifically, we recast the notion of stochastic two-scale convergence in the mean by introducing an appropriate stochastic unfolding operator. This operator admits similar properties as the periodic unfolding operator, leading to an uncomplicated method for stochastic homogenization. Secondly, we analyze the discrete-to-continuum (resp. stochastic homogenization) limit for a rate-independent system describing a network of linear elasto-plastic springs with random coefficients.