A DG/CR discretization for the variational phase-field approach to fracture

TL;DR

This paper introduces a novel discretization method using discontinuous elements for variational phase-field models of fracture, improving numerical robustness and isotropy in simulating crack propagation.

Contribution

It proposes a nonconforming discretization approach for displacement and damage fields, enhancing the numerical stability and accuracy of fracture simulations.

Findings

Demonstrates robustness across various examples

Improves isotropy in damage gradient approximation

Offers a versatile alternative to traditional finite element methods

Abstract

Variational phase-field models of fracture are widely used to simulate nucleation and propagation of cracks in brittle materials. They are based on the approximation of the solutions of free-discontinuity fracture energy by two smooth function: a displacement and a damage field. Their numerical implementation is typically based on the discretization of both fields by nodal $\mathbb{P}^1$ Lagrange finite elements. In this article, we propose a nonconforming approximation by discontinuous elements for the displacement and nonconforming elements, whose gradient is more isotropic, for the damage. The handling of the nonconformity is derived from that of heterogeneous diffusion problems. We illustrate the robustness and versatility of the proposed method through series of examples.