Stationary thermoelasticity and stochastic homogenization

Abstract

The aim of the paper is twofold: first, the stochastic homogenization theorem formulated by Dal Maso and Modica [9, 10] is extended to the case applicable to a class of nonlinear problems of mechanics. Second, this new theorem is applied to determine the effective thermoelastic response of the material body with stochastically periodic microstructure. As a result, one obtains the closed form of effective (homogenized) stored energy function. As a specific case, one-dimensional problem is solved analytically.