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A model for crack growth with branching and kinking

TitleA model for crack growth with branching and kinking
Publication TypePreprint
AuthorsRacca, S
quasistatic crack evolution, branching, kinking, Griffith\\\'s criterion

We study an evolution model for fractured elastic materials in the 2-dimensional case, for which the crack path is not assumed to be known a priori. We introduce a topology for the cracks suitable to remove the restrictions on the regularity of the crack set and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity at each of its points. By means of a time-discretization approach, we prove the existence of a continuous-time evolution that satisfies an energy inequality and a stability criterion. The energy balance also takes into account the energy dissipated at the front of the fracture. The stability criterion is stated in the framework of Griffith\\\'s theory, in terms of the energy release rate, when the crack grows at least at one point of its front.

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