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. 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.

A phase-field model for thermo-mechanical fracture with an open-source implementation of it using Gridap in Julia

“…One may consider the proposed model as an extension to the phasefield model for brittle fracture, presented by Dhas et al [1] from iso-thermal to a non-isothermal case. We have provided the details of an open-source implementation of the proposed model for various numerical examples using a newly developed finite element toolbox Gridap [38,39,40], in Julia [41,42]. Julia is a programming language with advantages of simple code formulation as in dynamic languages like MATLAB and high performance like static languages, e.g.…”