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Research Article | Open Access

Homogenization of stiff inclusions through network approximation

Université de Paris, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, 75205 Paris CEDEX 13 France
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Abstract

We investigate the homogenization of inclusions of infinite conductivity, randomly stationary distributed inside a homogeneous conducting medium. A now classical result by Zhikov shows that, under a logarithmic moment bound on the minimal distance between the inclusions, an effective model with finite homogeneous conductivity exists. Relying on ideas from network approximation, we provide a relaxed criterion ensuring homogenization. Several examples not covered by the previous theory are discussed.

Keywords

Stochastic homogenizationnetwork approximationhigh-contrast mediaeffective conductivityrandom inclusions
CLC number: 35R60, 94C05, 78M40

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Networks and Heterogeneous Media
Volume 17 Issue 2,
April 2022
Pages 163-202
DOI: 10.3934/nhm.2022002

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Cite this article:
Gérard-Varet D, Girodroux-Lavigne A. Homogenization of stiff inclusions through network approximation. Networks and Heterogeneous Media, 2022, 17(2): 163-202. https://doi.org/10.3934/nhm.2022002

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Received: 01 June 2021
Revised: 01 January 2022
Published: 15 April 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)