A model for crack growth with branching and kinking

Article type: Research Article

Authors: Racca, Simone

Affiliations: SISSA, Via Bonomea 265, 34136 Trieste, Italy. Tel.: +39 040 3787591; E-mail: smnrcc@yahoo.it

Abstract: 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.

Keywords: quasistatic crack evolution, dissipation, branching, kinking, Griffith's criterion

DOI: 10.3233/ASY-141233

Journal: Asymptotic Analysis, vol. 89, no. 1-2, pp. 63-110, 2014