Phase field modeling of complex crack patterns in multi-physics problems

Recently developed continuum phase field models for brittle fracture show excellent modeling capability in situations with complex crack topologies including branching in the small and large strain applications. This work presents a generalization towards fully coupled multi-physics problems at large strains. A modular concept is outlined for the linking of the diffusive crack modeling with complex multi field material response, where the focus is put on the model problem of finite thermo-elasticity. This concerns a generalization of crack driving forces from the energetic definitions towards stress-based criteria, the constitutive modeling of degradation of non-mechanical fluxes on generated crack faces. Particular assumptions are made on the generation of convective heat exchanges approximating surface load integrals of the sharp crack approach by distinct volume integrals. The coupling effect is also shown in generation of cracks due to thermally induced stress states. We finally demonstrate the performance of the phase field formulation of fracture at large strains by means of representative numerical examples. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)