Dynamic phase-field fracture with a first-order discontinuous Galerkin method for elastic waves

TL;DR

This paper introduces a novel numerical method combining discontinuous Galerkin and phase-field approaches to simulate wave-induced dynamic fracture in elastic materials, effectively capturing crack growth and wave reflections.

Contribution

It develops a new staggered time-stepping algorithm integrating hyperbolic wave equations with phase-field fracture modeling for the first time.

Findings

Effective simulation of crack growth and spalling phenomena.

Accurate modeling of wave reflections at diffusive interfaces.

Demonstrated advantages in 2D and 3D examples.

Abstract

We present a new numerical approach for wave induced dynamic fracture. The method is based on a discontinuous Galerkin approximation of the first-order hyperbolic system for elastic waves and a phase-field approximation of brittle fracture driven by the maximum tension. The algorithm is staggered in time and combines an implicit midpoint rule for the wave propagation followed by an implicit Euler step for the phase-field evolution. At fracture, the material is degraded, and the waves are reflected at the diffusive interfaces. Two and three-dimensional examples demonstrate the advantages of the proposed method for the computation of crack growth and spalling initiated by reflected and superposed waves.