A spatio-temporally adaptive asynchronous variational integrator for a phase field model of dynamic fracture

Phase field modeling of fracture is an effective approach for simulating crack propagation. However, the presence of a length scale parameter in the phase field model requires a uniformly fine mesh, leading to high computational costs, especially in dynamic simulations where the global time step is determined by the smallest spatial mesh element. A recently proposed asynchronous variational integrator (AVI) for the phase field modeling of dynamic fracture addresses this by allowing each spatial element to evolve with an independent time step. In this approach, mechanical fields are updated at every time step, while the phase field is updated only after the displacement update of the largest spatial mesh element, reducing the computational costs. We build upon this formulation by incorporating spatial adaptivity, refining the mesh based on a criterion guided by the phase field variable. This leads to a spatio-temporally adaptive AVI for the phase field model of dynamic fracture, with spatial adaptivity driven by the phase field evolution and temporal adaptivity inherently provided by the AVI. Benchmark studies show that the proposed method reduces computational costs while accurately capturing dynamic fracture behavior.