Periodic homogenization in scalar Hencky plasticity

Abstract

This paper investigates the periodic homogenization of a two-phase elasto-plastic material in the framework of $\Gamma$-convergence. It establishes the link between the homogenized functional and that which was previously obtained in [12] in the context of two-scale convergence. Although there is no gap between the two formulations and that involving two-scale has the hallmark of a (two-scale) elasto-plastic problem, we are unable to positively ascertain the elasto-plastic character of the homogenized energy except in a one-dimensional setting.