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/asy123300848nas a2200133 4500008004100000245009600041210006900137260003400206520037800240653002300618100001800641700001900659856003600678 2014 en d00aA variational model for the quasi-static growth of fractional dimensional brittle fractures0 avariational model for the quasistatic growth of fractional dimen bEuropean Mathematical Society3 aWe 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.

10aVariational models1 aRacca, Simone1 aToader, Rodica uhttp://hdl.handle.net/1963/698300403nas a2200109 4500008004100000245005300041210005300094260001000147653003300157100001800190856008500208 2013 en d00aSome models of crack growth in brittle materials0 aSome models of crack growth in brittle materials bSISSA10aQuasi-static crack evolution1 aRacca, Simone uhttps://www.math.sissa.it/publication/some-models-crack-growth-brittle-materials01110nas a2200109 4500008004100000245003900041210003600080260001000116520082000126100001800946856003600964 2012 en d00aA Viscosity-driven crack evolution0 aViscositydriven crack evolution bSISSA3 aWe 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 Griffithâ€™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.

1 aRacca, Simone uhttp://hdl.handle.net/1963/5130