Homogenization of a linear elastic body with rigid inclusions and a Robin type boundary conditions

TL;DR

This paper investigates the asymptotic behavior of a linear elastic material with periodically distributed rigid inclusions as their size diminishes, using two-scale convergence techniques to derive homogenized models under Robin boundary conditions.

Contribution

It provides a rigorous homogenization analysis for elastic bodies with rigid inclusions of the same order as the periodicity, under mixed boundary conditions.

Findings

Derived homogenized equations for elastic bodies with rigid inclusions

Proved convergence results using two-scale methods

Characterized the limit behavior under Robin boundary conditions

Abstract

This paper is devoted to study of the limiting behaviour of an elastic material with periodically distributed rigid inclusions of size {\epsilon}, as the small parameter {\epsilon} goes to zero. We address here the case with inclusions of the same size as the period of the structure. The body in consideration here is suppose to be clamped on one part of its exterior boundary and submitted to given tractions on the other. By means of the well known two-scale convergence techniques, one convergence result is proved.