Damage as Gamma-limit of microfractures in anti-plane linearized elasticity

TL;DR

This paper derives a homogenization model for brittle materials with microfractures, showing how damage emerges as a limit of microfracture distributions through Gamma-convergence.

Contribution

It introduces a Gamma-limit framework for modeling damage as the limit of microfractures in periodic brittle materials.

Findings

Damage modeled as Gamma-limit of microfractures

Three different limit models depending on parameters

Homogenization results for periodic brittle inclusions

Abstract

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence. In particular, damage is obtained as limit of periodically distributed microfractures.