@article {2013, title = {A model for crack growth with branching and kinking}, journal = {Asymptotic Analysis}, volume = {89}, year = {2014}, pages = {63-110}, publisher = {SISSA}, type = {Research Article}, chapter = {63}, 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{\textquoteright}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, branching, kinking, Griffith\\\'s criterion}, doi = {10.3233/ASY-141233}, url = {https://content.iospress.com/articles/asymptotic-analysis/asy1233}, author = {Simone Racca} } @article {10829, title = {A variational model for the quasi-static growth of fractional dimensional brittle fractures}, number = {Interfaces and Free Boundaries}, year = {2014}, publisher = {European Mathematical Society}, abstract = {

We propose a variational model for the irreversible quasi-static evolution of brittle fractures having fractional Hausdorff dimension in the setting of two-dimensional antiplane and plane elasticity. The evolution along such irregular crack paths can be obtained as $\Gamma$-limit of evolutions along one-dimensional cracks when the fracture toughness tends to zero.

}, keywords = {Variational models}, doi = {10.4171/IFB/328}, url = {http://hdl.handle.net/1963/6983}, author = {Simone Racca and Rodica Toader} } @mastersthesis {2013, title = {Some models of crack growth in brittle materials}, year = {2013}, school = {SISSA}, keywords = {Quasi-static crack evolution}, author = {Simone Racca} } @article {2012, title = {A Viscosity-driven crack evolution}, journal = {Advances in Calculus of Variations 5 (2012) 433-483}, number = {SISSA;63/2011/M}, year = {2012}, publisher = {SISSA}, abstract = {

We present a model of crack growth in brittle materials which couples dissipative effects on the crack tip and viscous effects. We consider the 2 -dimensional antiplane case with pre-assigned crack path, and firstly prove an existence result for a rate-dependent evolution problem by means of time-discretization. The next goal is to describe the rate-independent evolution as limit of the rate-dependent ones when the dissipative and viscous effects vanish. The rate-independent evolution satisfies a Griffith{\textquoteright}s criterion for the crack growth, but, in general, it does not fulfil a global minimality condition; its fracture set may exhibit jump discontinuities with respect to time. Under suitable regularity assumptions, the quasi-static crack growth is described by solving a finite-dimensional problem.

}, doi = {10.1515/acv-2011-0012}, url = {http://hdl.handle.net/1963/5130}, author = {Simone Racca} }