Accessible Unlicensed Requires Authentication Published by De Gruyter October 2, 2012

A viscosity-driven crack evolution

Simone Racca

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.

Received: 2011-11-29
Accepted: 2012-02-22
Published Online: 2012-10-02
Published in Print: 2012-10-01

© 2012 by Walter de Gruyter Berlin Boston