01687nas a2200145 4500008004100000245005600041210005400097260001000151300001100161490000700172520119700179653007701376100001801453856007001471 2014 en d00aA model for crack growth with branching and kinking0 amodel for crack growth with branching and kinking bSISSA a63-1100 v893 a

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 some general assumptions on the structure of the fracture sets suitable to remove the restrictions on the regularity of the crack sets and to allow for kinking and branching to develop. In addition we define the front of the fracture and its velocity. 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.

10aquasistatic crack evolution, branching, kinking, Griffith\\\'s criterion1 aRacca, Simone uhttps://content.iospress.com/articles/asymptotic-analysis/asy1233