A Phase Field Approach for Dynamic Fracture

In phase field fracture models cracks are indicated by the value of a scalar field variable which interpolates smoothly between broken and undamaged material. The evolution equation for this crack field is coupled to the mechanical field equations in order to model the mutual interaction between the crack evolution and mechanical quantities. In finite element simulations of crack growth at comparatively slow loading velocities, a quasi-static phase field model yields reasonable results. However, the simulation of fast loading or the nucleation of new cracks challenges the limits of such a formulation. Here, the quasi-static phase field model predicts brutal crack extension with an artificially high crack speed. In this work, we analyze to which extend a dynamic formulation of the mechanical part of the phase field model can overcome this paradox created by the quasi-static formulation. In finite element simulations, the impact of the dynamic effects is studied, and differences between the crack propagation behavior of the quasi-static model and the dynamic formulation are highlighted. (© 2013 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)