juliaPF

A finite element implementation of a variational phase-field model for fracture in Julia.

The script FEM.jl contains the Julia implementation of the quasi-static AT1 phase-field model with the volumetric-deviatoric split. Each time step is solved using the modified Newton scheme presented in

O. Lampron, D. Therriault, and M. Lévesque, “An efficient and robust monolithic approach to phase-field quasi-static brittle fracture using a modified Newton method,” Computer Methods in Applied Mechanics and Engineering, vol. 386, p. 114091, Dec. 2021, doi: 10.1016/j.cma.2021.114091.

A preprint of the paper is available at https://arxiv.org/abs/2109.05373.

The script main.jl contains the pre-processing and settings of the problem. It calls the functions of FEM.jl.

This work was originally developped for the aforementionned publication. If you use this work, please cite this paper.

Dependencies and usage

FEM.jl relies on the Pardiso and WriteVTK library. You can add them to your environment using, in the Julia session, the command Pkg.add("Pardiso") or Pkg.add("WriteVTK"). You might need to build Pardiso after adding the package with the command Pkg.build("Pardiso"). For more detail see the Pardiso.jl package documentation (https://github.com/JuliaSparse/Pardiso.jl).

To run a simulation, 2 options are available:

1. • Open a terminal and place yourself in the directory containing the mesh files, the FEM.jl script and main.jl script.
   • Open a Julia session (if properly installed, on Linux, simply call julia. Otherwise see Julia documentation).
   • To read and compile the FEM.jl script, execute: include("FEM.jl").
   • To launch the simulation, execute: include("main.jl").
2. If you are using Atom (text editor) and Juno (Atom environment for the Julia language), then simply:
   • Open and execute the FEM.jl file with Atom+Juno (Ctrl + Shift + Enter to execute the file).
   • Open and execute the main.jl file with Atom+Juno (Ctrl + Shift + Enter to execute the file).

Validation

The validation file contains the solution obtained for the SENP-shear test with the implemented model. The force-displacement solution is compared with results from the literature.

Geometries

Geometries contains the mesh used for multiple geometries or benchmarks:

• Single-edge notched plate submitted to tensile (SENP-tensile).
• Single-edge notched plate submitted to shear (SENP-shear).
• Three-point bending notched beam (3Point-n).
• L-shaped panel (L-shaped).
• Notched bilayer (Bilayer).

Notes

This project is licensed under the terms of the MIT license (see LICENSE.txt).

Author: Olivier Lampron