The Phase-Field Approach to Brittle Fracture: Theory and Numerical Implementation

Welcome to the companion repository for the short course "The Phase-Field Approach to Brittle Fracture: Theory and Numerical Implementation" presented at the 18th U.S. National Congress on Computational Mechanics.

This repository contains two primary Jupyter notebook files that demonstrate single edge notch test simulations:

1. AT1 Model Implementation
2. Phase-Field Model Implementation

Both notebooks are designed to:

• Run seamlessly in Google Colab (as demonstrated in the course)
• Execute in local Jupyter environments
• Provide step-by-step implementation guidance
• Include detailed comments and explanations

📁 installation-guide/FEniCSx_Installation_Guide.pdf

A comprehensive installation guide covering:

• FEniCSx installation on Windows 11 using Docker
• FEniCSx installation on macOS using Conda

Note: You do NOT need to install FEniCSx to run the Jupyter notebook files in this repository. The notebooks are designed to work directly in Google Colab with all dependencies pre-configured. However, you may need this installation guide if you want to run FEniCSx simulations on your personal laptop or computer for future projects.

1. Click on the notebook files in this repository
2. Select "Open in Colab"
3. Follow the in-notebook setup instructions
4. Run cells sequentially

1. Follow the appropriate installation guide for your operating system
2. Clone this repository: git clone https://github.com/farhadkama/[phasefield_usnccm]
3. Navigate to the repository directory
4. Launch Jupyter: jupyter notebook
5. Open and run the desired notebook

For continued learning and advanced applications in phase-field modeling, you can explore these repositories:

FEniCSx_Kamarei_Kumar_Lopez-Pamies

An educational repository focused on learning phase-field modeling from fundamentals to advanced concepts [1].

FEniCSx_Kamarei_Lopez-Pamies

A specialized repository containing benchmark problems and advanced modeling approaches [2].

For any inquiry, please contact me at kamarei2@illinois.edu

Alternatively, you may also reach out to my Ph.D. advisor at pamies@illinois.edu

[1] Kamarei, F., Kumar, A., Lopez-Pamies, O. (2024). The poker-chip experiments of synthetic elastomers explained. Journal of the Mechanics and Physics of Solids, 188, 105683. PDF

[2] Kamarei, F., Zeng, B., Dolbow, J.E., Lopez-Pamies, O. (2026). Nine circles of elastic brittle fracture: A series of challenge problems to assess fracture models. Computer Methods in Applied Mechanics and Engineering, 448, 118449. PDF