A remark about the periodic homogenization of certain composite fibered media - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Networks and Heterogeneous Media Année : 2020

A remark about the periodic homogenization of certain composite fibered media

Résumé

We explain in this paper the similarity arising in the homogenization process of some composite fibered media with the problem of the reduction of dimension 3d − 1d. More precisely, we highlight the fact that when the homogenization process leads to a local reduction of dimension, studying the homogenization problem in the reference configuration domain of the composite amounts to the study of the corresponding reduction of dimension in the reference cell. We give two examples in the framework of the thermal conduction problem: the first one concerns the reduction of dimension in a thin parallelepiped of size ε containing another thinner parallelepiped of size rε ε playing a role of a "hole". As in the homogenization, the one-dimensional limit problem involves a "strange term". In addition both limit problems have the same structure. In the second example, the geometry is similar but now we assume a high contrast between the conductivity (of order 1) in the small parallelepiped of size rε := rε, for some fixed r (0 < r < 1 2) and the conductivity (of order ε 2) in the big parallelepiped of size ε. We prove that the limit problem is a nonlocal problem and that it has the same structure as the corresponding periodic homogenized problem.
Fichier principal
Vignette du fichier
MS-Last version version.pdf (174.26 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03662190 , version 1 (09-05-2022)

Identifiants

Citer

François Murat, Ali Sili. A remark about the periodic homogenization of certain composite fibered media. Networks and Heterogeneous Media, 2020, 15 (1), pp.125-142. ⟨10.3934/nhm.2020006⟩. ⟨hal-03662190⟩
71 Consultations
26 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More