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

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. This 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. Tests on a single-edge notched plate under tension, an L-shaped panel, a notched plate with a hole, a notched beam under symmetric three-point bending and a notched beam with three holes under asymmetric three-point bending are considered to demonstrate how the proposed Gridap-based phase-field Julia code can be used to simulate fracture in brittle materials.