Homogenization of stiff inclusions through network approximation

TL;DR

This paper explores the homogenization of highly conductive inclusions in a medium, using network approximation to relax previous conditions and include new cases.

Contribution

It introduces a relaxed criterion for homogenization based on network approximation, expanding the applicability beyond Zhikov's classical results.

Findings

Established a new criterion for homogenization of infinite conductivity inclusions.

Provided examples where previous conditions do not apply but homogenization still holds.

Extended the theoretical framework for modeling conductive composites.

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 inter-particle distance, 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.