Damage Growth As An Interface Problem : the Thick Level Set (Tls) Approach

Abstract eng:
In this paper, we introduce 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, we assume the material to be 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 thatdamage front is non local in the sense that it averages information over the thickness in the wake of the front. The damage model may be of course dysimmetric, i.e., keeping stiffness in compression. A few important theoretical advantages of the proposed approach are as follows : • The zone for which the materials is fully damaged is located inside a clearly identified domain (given by an iso- level set). • The non-locality steps in gradually in the model. At initiation the model is fully local. This is in accordance with the fact that non locality is the results of micro-cracks interaction. At initiation, micro-cracks being absent no length scale should prevail. • The dissipation in the proposed model is proved to be trivially positive. This proof is not always straightforward with other nonlocal models as integral non local damage models. Numerical examples were already described in [1] but new and more complex examples will be shown at the conference demonstrating the capability of the new model to initiate cracks and propagate them even in complex topological patterns (branching and merging for instance).

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