AT2 Phase-Field Fracture Simulation (FEniCS)

This repository provides a simple and modular implementation of the AT2 phase-field fracture model using the open-source finite element library FEniCS. The code is structured for clarity and educational purposes, allowing researchers and students to explore the basic ideas behind the phase-field method for brittle fracture.

If you are a beginner in FEniCS, you can learn more through my course here: abhigupta.io/fenics-workshop

Overview

This implementation includes:

• The AT2 phase-field fracture model for brittle materials
• Elastic energy decomposition into tensile and compressive parts
• Quasi-static displacement loading
• Configurable material and simulation parameters
• Output written in XDMF format for visualization in ParaView

Citations

If you find this code useful, please cite the following works:

1. Gupta, A., Krishnan, U. M., Mandal, T. K., Chowdhury, R., & Nguyen, V. P. (2022).
   An Adaptive Mesh Refinement Algorithm for Phase-Field Fracture Models: Application to Brittle, Cohesive, and Dynamic Fracture.
   Computer Methods in Applied Mechanics and Engineering, 399, 115347.
   DOI: 10.1016/j.cma.2022.115347

2. Gupta, A., Krishnan, U. M., & Chowdhury, R. (2020).
   An Auto-Adaptive Sub-Stepping Algorithm for Phase-Field Modeling of Brittle Fracture.
   Theoretical and Applied Fracture Mechanics, 108, 102622.
   DOI: 10.1016/j.tafmec.2020.102622

3. Gupta, A., Nguyen, D. T., Hirshikesh, & Duddu, R. (2024).
   Damage Mechanics Challenge: Predictions from an Adaptive Finite Element Implementation of the Stress-Based Phase-Field Fracture Model.
   Engineering Fracture Mechanics, 306, 110252.
   DOI: 10.1016/j.engfracmech.2024.110252

4. Bijaya, A., Gupta, A., Krishnan, U. M., & Chowdhury, R. (2024).
   A Multilevel Adaptive Mesh Scheme for Efficient Simulation of Thermomechanical Phase-Field Fracture.
   Journal of Engineering Mechanics, 150(6), 04024029.
   DOI: 10.1061/JENMDT.EMENG-7480

5. Krishnan, U. M., Gupta, A., Kumar, A., & Chowdhury, R. (2024).
   Adaptive PF-CZM for Multiphysics Fracture Analysis in Functionally Graded Materials.
   Engineering Fracture Mechanics, 310, 110461.
   DOI: 10.1016/j.engfracmech.2024.110461

6. Krishnan, U. M., Gupta, A., & Chowdhury, R. (2022).
   Adaptive Phase-Field Modeling of Brittle Fracture Using a Robust Combination of Error-Estimator and Markers.
   Engineering Fracture Mechanics, 274, 108758.
   DOI: 10.1016/j.engfracmech.2022.108758

7. Mandal, T. K., Gupta, A., Nguyen, V. P., Chowdhury, R., & De Vaucorbeil, A. (2020).
   A Length Scale Insensitive Phase-Field Model for Brittle Fracture of Hyperelastic Solids.
   Engineering Fracture Mechanics, 236, 107196.
   DOI: 10.1016/j.engfracmech.2020.107196

8. Modak, A., Krishnan, U. M., Gupta, A., Gangwar, T., & Chowdhury, R. (2024).
   Sparse Polynomial Chaos Expansion and Adaptive Mesh Refinement for Enhanced Fracture Prediction Using the Phase-Field Method.
   Theoretical and Applied Fracture Mechanics, 133, 104639.
   DOI: 10.1016/j.tafmec.2024.104639

9. Nguyen, D. T., Gupta, A., Duddu, R., & Annavarapu, C. (2025).
   An Adaptive Mesh Refinement Algorithm for Stress-Based Phase-Field Fracture Models for Heterogeneous Media: Application Using FEniCS to Ice-Rock Cliff Failures.
   Finite Elements in Analysis and Design, 244, 104311.
   DOI: 10.1016/j.finel.2024.104311

Running the Code via Docker

You can run the code using Docker without installing FEniCS manually.

1. Install FEniCS

After installing and starting Docker, open your terminal and pull the FEniCS image:

docker pull iitrabhi/fenics_notebook

2. Launch the FEniCS Notebook Server

Start the Jupyter Notebook server with the following command:

docker run -p 8888:8888 -v host_system_path:/root/ -w /root/ iitrabhi/fenics_notebook

Note: Replace host_system_path with the full path to the folder containing your code.
For example, if your code is located in D:\Codes, run:

docker run -p 8888:8888 -v D:\Codes:/root/ -w /root/ iitrabhi/fenics_notebook

Once the container starts, copy the Jupyter Notebook URL shown in the terminal and open it in your web browser.

🤝 Collaborations

I am always open to research and development collaborations in computational mechanics and multi-physics simulations. Feel free to reach out to me on LinkedIn to discuss potential opportunities or joint projects.

⚖️ License

This project is released under the MIT License. If you use this repository or build upon it in your research, please cite the relevant papers listed above.