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.

PB - SISSA VL - 89 UR - https://content.iospress.com/articles/asymptotic-analysis/asy1233 IS - 1-2 U1 - 6293 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A variational model for the quasi-static growth of fractional dimensional brittle fractures Y1 - 2014 A1 - Simone Racca A1 - Rodica Toader KW - Variational models AB -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.

PB - European Mathematical Society UR - http://hdl.handle.net/1963/6983 U1 - 6973 U2 - Mathematics U4 - -1 ER - TY - THES T1 - Some models of crack growth in brittle materials Y1 - 2013 A1 - Simone Racca KW - Quasi-static crack evolution PB - SISSA U1 - 7205 U2 - Mathematics U4 - 1 U5 - MAT/05 ANALISI MATEMATICA ER - TY - JOUR T1 - A Viscosity-driven crack evolution JF - Advances in Calculus of Variations 5 (2012) 433-483 Y1 - 2012 A1 - Simone Racca AB -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 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.

PB - SISSA UR - http://hdl.handle.net/1963/5130 U1 - 4944 U2 - Mathematics U3 - Functional Analysis and Applications U4 - -1 ER -