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Threshold based quasi-static evolution for damage

Adriana Garroni (Univeristé de Rome, La Sapienza)

We consider a variational model for elastic damage proposed by Francfort and Marigo. This energy based model is nonconvex since only to extreme states (damaged and undameged material) are possible, and in the minimization procedure microstructures can be produced. A relaxed incremental problem that accounts for irreversibility can be defined and, by means of time discretization, a relaxed quasi-static evolution can be obtained. This relaxed quasi-static evolution accounts for a damage process that in principle in completely predictive and does not require any a priori assumption on the damage path. We give an alternative model for damage based on a threshold criterion. We prove that an ’energy based’ solution is also a ’threshold’ solution. As a byproduct we also obtain that local minimizers for the energy based model are actually global minimizers.

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