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GT CalVa V Crismale

Lundi 30 janvier 2017

Vito CRISMALE (CMAP, Ecole Polytechnique)

Cohesive fracture : irreversible quasistatic evolution for a model subject to fatigue

Abstract : This talk concerns the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity.
While in brittle fracture the energy dissipated in the fracture process depends only on the ((n-1)-dimensional) measure of the crack set, in cohesive fracture other characteristic of the fracture, as the jump between the two lips of the crack, influence the dissipation of energy.
The main feature of our model is that this dissipated energy depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e., a complete fracture may be produced by oscillation of small jumps.
The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-time incremental minimum problems. The main difficulty in the passage to the continuous-time limit is that one lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. I will explain how, eventually, after proving the existence in this weak formulation, we are able to improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement.