A phase-field description of dynamic brittle fracture

In contrast to discrete descriptions of fracture, phase-field descriptions do not require numerical tracking of discontinuities in the displacement field. This greatly reduces implementation complexity. In this work, we extend a phase-field model for quasi-static brittle fracture to the dynamic case. We introduce a phase-field approximation to the Lagrangian for discrete fracture problems and derive the coupled system of equations that govern the motion of the body and evolution of the phase-field. We study the behavior of the model in one dimension and show how it influences material properties. For the temporal discretization of the equations of motion, we present both a monolithic and staggered time integration scheme. We study the behavior of the dynamic model by performing a number of two and three dimensional numerical experiments. We also introduce a local adaptive refinement strategy and study its performance in the context of locally refined T-splines. We show that the combination of the phase-field model and local adaptive refinement provides an effective method for simulating fracture in three dimensions.