This repository provides a toolkit for performing Finite Element Method (FEM) simulations on 2D/3D geometries, with two complementary implementations:
- A MATLAB-based version for prototyping and accessibility.
- A high-performance Fortran-based version suitable for large-scale simulations and integration with open-source toolchains.
The code is demonstrated on a soft 2D/3D structures deforming under applied forces, but is general enough to be adapted for arbitrary 2D/3D triangulated domains.
Documentation containing implementation details are in the `doc` branch. However it is very basic and a work in progress.
While MATLAB offers ease of use, the Fortran implementation is designed for efficiency and openness, utilizing freely available tools for meshing (GMSH), solving (Fortran), and visualization (PyVista/ParaView). The Fortran version is approximately 60× faster than its MATLAB counterpart, making it suitable for extensive simulations or future coupling with external solvers.
The implementations follow the formulations described in the following works:
- Bhattacharya, A., & Balazs, A. C. (2013). Stiffness-modulated motion of soft microscopic particles over active adhesive cilia. Soft Matter, 9(15), 3945–3955.
- Duki, S. F., et al. (2011). Modeling the nanoscratching of self-healing materials. J. Chem. Phys., 134(8), 084901.
These formulations can be adapted to model a variety of soft structures interacting with applied forces or embedded in dynamic environments.
flexFEM/
├── fortran/ # High-performance implementation using Fortran and GMSH
├── matlab/ # MATLAB implementation with educational focus
├── LICENSE
└── README.md # (This file)
Each subdirectory includes a separate README file with detailed instructions for compilation, simulation, and visualization.
- Requires
gfortran, GMSH (compiled from source), and optionallycondafor setting up Python-based visualization tools (PyVista). - Compilation and execution are handled via a
Makefileand shell scripts. - Outputs VTK files for ParaView-based visualization.
➡ See fortran/README.md for setup and usage instructions.
- Requires MATLAB R2020b or newer (for
pagemtimes) and a working GMSH installation. - Suitable for quick experimentation and understanding of FEM concepts.
- Outputs PNG plots and optionally VTK files.
➡ See matlab/README.md for setup and usage instructions.
This repository is released under the MIT License. You are free to use, modify, and distribute the code with proper attribution.
Contributions, bug reports, and feature suggestions are welcome. Please open an issue or submit a pull request.