Inserted: 28 nov 2011
Last Updated: 15 feb 2013
Journal: Adv. Calc. Var.
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.
Keywords: vanishing viscosity, Viscoelasticity, Quasi-static crack evolution, Griffith’s criterion, Rate-dependent evolution, Rate-indipendent evolution