Title | A Viscosity-driven crack evolution |

Publication Type | Journal Article |

Year of Publication | 2012 |

Authors | Racca, S |

Journal | Advances in Calculus of Variations 5 (2012) 433-483 |

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’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. |

URL | http://hdl.handle.net/1963/5130 |

DOI | 10.1515/acv-2011-0012 |

## A Viscosity-driven crack evolution

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