Calculus of Variations and Geometric Measure Theory

D. Knees - A. Mielke - C. Zanini

Crack growth in polyconvex materials

created by zanini on 05 Aug 2008
modified on 27 Jul 2011


Published Paper

Inserted: 5 aug 2008
Last Updated: 27 jul 2011

Journal: Phys. D
Volume: 239
Pages: 1470-1484
Year: 2010

WIAS Preprint 1351


We discuss a model for crack propagation in an elastic body, where the crack path is described a-priori. In particular, we develop in the framework of finite-strain elasticity a rate-independent model for crack evolution which is based on the Griffith fracture criterion. Due to the nonuniqueness of minimizing deformations, the energy-release rate is no longer continuous with respect to time and the position of the crack tip. Thus, the model is formulated in terms of the Clarke differential of the energy, generalizing the classical crack evolution models for elasticity with strictly convex energies. We prove the existence of solutions for our model and also the existence of special solutions, where only certain extremal points of the Clarke differential are allowed.

Keywords: finite-strain elasticity, Rate-independent problems, local energetic solution, parameterized solutions