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
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 [ ])
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