Two-scale analysis of a non standard transmission problem in two-component media

TL;DR

This paper uses two-scale homogenization to derive a macroscopic heat flow model in two-component media with adhesive contact, simplifying the complex microstructure into a single-phase elliptic equation.

Contribution

It introduces a two-scale convergence approach for homogenizing heat flow in media with adhesive contact, resulting in a simplified macroscopic model.

Findings

Homogenization yields a single-phase elliptic equation at the macro level.

The micro-model is based on mass conservation with adhesive interfacial contact.

The approach effectively captures the influence of microstructure on heat flow.

Abstract

In this short paper, periodic homogenization of a steady heat flow in two-component media with highly adhesive contact is performed via the two-scale convergence technique. Our micro-model is based on mass conservation for the heat flow in each phase with interfacial contact of adhesive type between these constituents. It is shown that the macroscopic model is a single phase elliptic equation.