Homogenization of heat diffusion in a cracked medium

TL;DR

This paper introduces a homogenization method for heat diffusion in cracked materials, showing that cracks induce a source term in the effective equation, with assumptions on crack geometry and arrangement.

Contribution

It presents a novel homogenization approach accounting for crack-induced sources in heat diffusion through periodically cracked media.

Findings

Cracks induce a source term in the homogenized heat equation.

The method applies to cracks orthogonal to the surface with periodic arrangement.

Effective model captures the influence of crack geometry on heat diffusion.

Abstract

We develop in this note a homogenization method to tackle the problem of a diffusion process through a cracked medium. We show that the cracked surface of the domain induces a source term in the homogenized equation. We assume that the cracks are orthogonal to the surface of the material, where an incoming heat flux is applied. The cracks are supposed to be of depth 1, of small width, and periodically arranged.