Damage dynamics, $G$-Convergence, Homogenization in dynamics, Threshold Conditions

TL;DR

This paper develops a variational approach to model elastodynamics with damage, resulting in a wave equation with time-dependent elastic coefficients that incorporate damage effects and satisfy a threshold condition.

Contribution

It introduces a novel variational formulation for elastodynamics with damage, linking dynamic damage evolution to quasi-static threshold conditions.

Findings

Wave equation with damage-dependent elastic coefficients

Solution construction via variational methods

Threshold condition consistent with quasi-static damage evolution

Abstract

In this paper we construct, by means of a variational formulation, the solutions of a problem of elastodynamics which includes the effect of damage for the elastic material. The result is a wave equation with time dependent operators which represents the elastic coefficients of the material undergoing damage. The dynamics that we construct also satisfies a threshold condition with the same threshold value that characterizes the quasi-static evolution of damage (see \cite{GL}).