Stochastic unfolding and homogenization of spring network models

TL;DR

This paper develops a stochastic unfolding method to homogenize energy-driven problems with rapidly oscillating random coefficients, extending periodic unfolding to stochastic settings and analyzing spring network models.

Contribution

It introduces a stochastic unfolding operator for homogenization and applies it to analyze the discrete-to-continuum limit of random spring networks.

Findings

Established a stochastic two-scale convergence in the mean.

Provided a simplified stochastic homogenization procedure.

Analyzed the limit behavior of a network of linear elasto-plastic springs with randomness.

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.