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

TL;DR

This paper introduces an asynchronous variational integrator for the phase field method in dynamic fracture modeling, enabling efficient computation and accurate fracture prediction without tracking crack topology.

Contribution

It adapts AVI to the phase field approach, allowing different mesh elements to have independent time steps, improving computational efficiency in dynamic fracture simulations.

Findings

Significantly speeds up computational efficiency.

Successfully captures complex dynamic fracture behaviors.

Compatible with AT1 and AT2 phase field models.

Abstract

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