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.

A phase-field model for thermo-mechanical fracture

“…One may consider the proposed model as an extension to the phase-field model for brittle fracture, presented by Dhas et al [33] from isothermal 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 [34][35][36] in Julia [37,38]. 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., C or FORTRAN.…”

Analysis on scattering characteristics of SH guided wave due to V-notch in a piezoelectric bi-material strip

“…For advanced materials and structures, processing errors or long-term use can lead to notch problem in the boundaries. By the tests on a notched plate, Rahaman [20] used Gridap-based phase-field Julia code to simulate fracture in brittle materials. Yu et al [21] performed an accurate fracture analysis of multi-material V-notched Reissner plates under bending or twisting.…”

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

“…Despite this, the phase-field model has gained a lot of popularity because it can easily be implemented in any commercially available finite element (FE) software [49][50][51][52][53][54]. Recently, there are also attempts toward developing open-source codes for the implementation of the phase-field models for fracture under mechanical loading [55][56][57] and thermo-mechanical loading [58,59], to make the models available to a wider class of researchers and practitioners. But to the best of the authors' knowledge, there is no open-source implementation of a phase-field model for electro-mechanical fracture.…”