Handling localization in damage models with the thick level set approach (TLS)

In this paper, we discuss a new way to model damage growth in solids. A level set is used to separate the undamaged zone from the damaged zone. In the damaged zone, the damage variable is an explicit function of the level set. This function is a parameter of the model. Beyond a critical length, it is assumed that the material is totally damaged, thus allowing a straightforward transition to fracture. The damage growth is expressed as a level set propagation. The configurational force driving the damage front is non local in the sense that it averages information over the thickness in the wake of the front. Three important theoretical advantages of the proposed approach are as follows: (a) The zone for which the materials is fully damaged is located inside a clearly identified domain (given by an iso-level set). (b) The non-locality steps in gradually in the model. At initiation the model is fully local. At initiation, micro-cracks being absent no length scale should prevail. (c) It is straightforward to prove that dissipation is positive. A numerical experiment of the cracking of a multiply perforated plate is discussed.