A new approach of graded damage modelling

Abstract

To prevent the problem of spurious localisation in damage mechanics, it is necessary to control the damage gradient amplitude. The body is decomposed in three domains: the undamaged body where ([Formula: see text]), the transition zone ([Formula: see text]) and the totally broken body ([Formula: see text]). For the thick level set (TLS) model, damage is a function of the signed distance to the surface [Formula: see text]. In this article, we propose to control the damage gradient using a convex internal constraint. This point of view produces a new description of graded damage. Analytical solutions on spheres and cylinders under radial loading are given and discussed. For particular internal constraints, the TLS results are recovered.