A new approach of graded damage modelling

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 presented.)), the transition zone ((Formula presented.)) and the totally broken body ((Formula presented.)). For the thick level set (TLS) model, damage is a function of the signed distance to the surface (Formula presented.). 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.