Homogenization of an elastic double-porosity medium with imperfect interface via the periodic unfolding method

Iulian Ţenţea,Patrizia Donato

doi:10.1186/1687-2770-2013-265

Abstract

We study an e-periodic model of a medium with double porosity which consists of two components, one of them being connected. We assume that the elasticity of the medium in the inclusion is of order e 2 and also, on the interface between the two components, we consider a jump of the displacement vector condition, proportional to the stress tensor which is continuous. The aim of the paper is to prove the convergence of the homogenization process using the periodic unfolding method.

Highlights

This paper deals with the homogenization of a double porosity model in elasticity describing a medium occupying an open set Ω in RN which consists of two components, one of them being connected and the second one disconnected
Using the periodic unfolding method, we prove some convergence results and describe the homogenized problems
In [ ] Donato et al use the periodic unfolding method for a two-component domain similar to the one considered in this paper

Summary

Introduction

This paper deals with the homogenization of a double porosity model in elasticity describing a medium occupying an open set Ω in RN which consists of two components, one of them being connected and the second one disconnected. Using the periodic unfolding method, we prove some convergence results and describe the homogenized problems. In [ ] Donato et al use the periodic unfolding method for a two-component domain similar to the one considered in this paper. The pioneering paper for the heat diffusion in a two-component domain with similar jump conditions on the interface is due to Auriault and Ene [ ] (see [ ], where the results were proved using asymptotic expansions). The main difficulty when applying the periodic unfolding method consists in finding suitable test functions adapted to our elasticity tensor and to the interface term appearing. For the case of periodically perforated domains, we refer to Léné [ ] (see [ ])

The domain

Periodic unfolding operators in two-component domain

Homogenization results In the following we will use the notation