An asynchronous variational integrator for the phase field approach to dynamic fracture

The phase field approach is widely used to model fracture behaviors due the absence of need track crack topology and ability predict nucleation branching. In this work, asynchronous variational integrator (AVI) adapted for dynamic brittle fracture. AVI derived from Hamilton's principle allows each element in mesh have its own local time step that may be different others'. While displacement explicitly updated, implicitly solved, with upper lower bounds strictly conveniently enforced. particular, two important variants approach, AT1 AT2 models, are equally easily implemented. Several benchmark problems study performances both results show significantly speeds up computational efficiency successfully captures complicated behavior.