A viscosity-driven crack evolution

作者：Racca Simone^*

来源：Advances in Calculus of Variations, 2012, 5(4): 433-483.

DOI：10.1515/acv-2011-0012

• Vanishing viscosity
• viscoelasticity
• rate dependent evolution
• rate independent evolution
• quasi-static crack evolution
• Griffith%26apos
• s criterion

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%26apos;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.

• 出版日期2012-10