On a microstructural model of damage in solids

Abstract

The aim of the paper is to outline and discuss some ideas and preliminary results concerning microstructural modelling of brittle-like damage in solids. We argue that the basic premises of the simple microelastic theory (independent micro-dilatation of particles), developed by S. Cowin et al. and the author, are a natural starting point in developing certain continuum damage mechanics models. In the brittle-like case under study, with the assumption of isotropic deterioration, the damage rate is added to the arguments (strain, damage and damage gradient) of the elastic energy density. The additional field quantity of the theory—the damage parameter in our context—leads to the appearance of hyperstresses and a balance equation for them. It is shown that the latter can be conveniently identified with the well-known Kachanov's law of damage growth. Thus this law, traditionally introduced through purely phenomenological arguments, finds a natural place in the herein proposed damage model as an equation expressing hyperstress equilibrium.