An open-source implementation of a phase-field model for brittle fracture using Gridap in Julia

TL;DR

This paper presents an open-source Julia implementation of a phase-field model for brittle fracture using Gridap, enabling flexible, memory-efficient simulations of crack propagation without re-meshing.

Contribution

It introduces a novel, user-friendly, and low-memory implementation of phase-field fracture modeling in Julia with Gridap, overcoming traditional discrete approach limitations.

Findings

Successfully simulated crack propagation in notched beams

Demonstrated flexibility and efficiency of the Gridap-based code

Validated the model with symmetric and asymmetric three-point bending tests

Abstract

This article proposes an open-source implementation of a phase-field model for brittle fracture using a recently developed finite element toolbox, Gridap in Julia. The present work exploits the advantages of both the phase-field model and Gridap toolbox for simulating fracture in brittle materials. On one hand, the use of the phase-field model, which is a continuum approach and uses a diffuse representation of sharp cracks, enables the proposed implementation to overcome such well-known drawbacks of the discrete approach for predicting complex crack paths as the need for re-meshing, enrichment of finite element shape functions and an explicit tracking of the crack surfaces. On the other hand, the use of Gridap makes the proposed implementation very compact and user-friendly that requires low memory usage, and provides a high degree of flexibility to the users in defining weak forms of partial differential equations. A test on a notched beam under symmetric three-point bending and a set of tests on a notched beam with three holes under asymmetric three-point bending is considered to demonstrate how the proposed Gridap based phase-field Julia code can be used to simulate fracture in brittle materials.