On damage theory of a cohesive medium

Abstract

A micro-mechanics damage model is proposed based on homogenization of penny-shaped cohesive micro-cracks (Barenblatt–Dugdale type) in a three dimensional representative volume element. By assuming that macro-hydrostatic stress state has dominant effect on permanent crack opening, a class of pressure sensitive yielding potentials and corresponding damage evolution laws have been derived. The merits of this class of damage models are: (1) Its ability to model and predict material failure and degradation due to cohesive micro-crack growth; (2) its ability to estimate the influence of Poisson's ratio on material's damage. One of the distinguished features of the new damage model is at macro-level the reversible part of effective constitutive relation is characterized as a nonlinear elasticity, whereas the irreversible part of effective constitutive relation is a form of pressure-sensitive plasticity, both of which are significantly different from material's behaviors at micro-level before homogenization.