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