Asymptotic analysis of stratified elastic media in the space of functions with bounded deformation

Abstract

We consider a heterogeneous elastic structure which is stratified in some direction. We derive the limit problem under the assumption that the Lamé coefficients and their inverses weakly* converge to Radon measures. Our method applies also to linear second-order elliptic systems of partial differential equations and in particular, for the case $d=1$, this addresses the previously open problem of determining the asymptotic behaviour in this context for the general anisotropic heat equation.