Hyperbolic phase field modeling of brittle fracture: Part I—Theory and simulations

We propose a new phase field model of dynamic brittle fracture, in which material damage evolves according to a hyperbolic partial differential equation. This model can be stably discretized using explicit time integration, without imposing crippling time step restrictions with refinement in space. The model is derived from microforce balance by including effects of microscopic inertia. Quantitative predictions of the proposed model differ from those of parabolic and elliptic phase field models in that there is a mild rate-toughening effect, but major qualitative solution features are essentially the same. We compute finite element approximations of solutions to several dynamic fracture scenarios to support these claims. Part II of this series will incorporate the proposed model into a hybrid isogeometric–meshfree framework for air-blast–structure interaction and provide further demonstrations of the model's physical and numerical properties.