Crack growth in polyconvex materials
- Knees, Dorothee
- Zanini, Chiara
- Mielke, Alexander
2010 Mathematics Subject Classification
- 74B20 74R10 74G65, 49L25, 49J40, 35K90
- rate-independent problems, energetic formulation, time-incremental minimization, parameterized solutions, energy-release rate, Griffith fracture criterion, finite-strain elasticity, local energetic solution
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.
- Phys. D, 239 (2010) pp. 1470--1484.