@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}
}