# EasyFEA documentation

![EasyFEA banner](_static/EasyFEA_banner.jpg)

## 🧭 Overview

**EasyFEA** is a user‑friendly Python library that simplifies finite element analysis by abstracting complex PDE formulations. It is flexible and supports a range of linear and nonlinear simulations with minimal setup. You will find below the finite element analysis that you can conduct using EasyFEA:

1. {doc}`Linear elastic simulations <examples/LinearizedElasticity/index>`: ``static``, ``dynamic``, ``contact``, ``homogenization`` and ``mesh optimization``.
2. {doc}`Hyperelastic simulations <examples/Hyperelasticity/index>`: ``static`` and ``dynamic`` in the ``Lagrangian`` framework.
3. {doc}`Euler-Bernoulli and Timoshenko beam simulations <examples/Beam/index>`: ``static``.
4. {doc}`Thermal simulations <examples/Thermal/index>`: ``static`` and ``transient``.
5. {doc}`Phase-field damage simulations for quasi-static brittle fracture <examples/PhaseField/index>`: advanced ``2D`` and ``3D`` simulations for ``isotropic``, ``transversely isotropic``, and ``anisotropic`` materials.
6. {doc}`Weak forms simulations <examples/WeakForms/index>`: ``static``, ``transient`` and ``dynamic`` for ``linear`` or ``non-linear`` problems.
7. {doc}`Digital Image Correlation (DIC) analyses <examples/DIC/index>`.
8. [Parameter identification](https://gitlab.univ-eiffel.fr/collaboration-msme-fcba/spruce-params).
9. [Stochastic phase-field simulations](https://gitlab.univ-eiffel.fr/collaboration-msme-fcba/spruce-stochastic).

📸 Explore the interactive **{doc}`gallery <gallery/index>`** to visualize simulation results.

For each simulation, users create a {py:class}`~EasyFEA.FEM._mesh.Mesh` and a {py:class}`~EasyFEA.Models._IModel`. Once the simulation has been set up, defining the boundary conditions, solving the problem and visualizing the results is straightforward.

Numerous examples of mesh creation are available in the  {doc}`/examples/Meshes <examples/Meshes/index>` gallery.

The simplest and quickest introduction is available in the {ref}`begin`.

## ⚖️ License

Copyright (C) 2021-2024 Université Gustave Eiffel.
Copyright (C) 2025-2026 Université Gustave Eiffel, INRIA.

EasyFEA is distributed under the terms of the [GNU General Public License v3.0 only](https://spdx.org/licenses/GPL-3.0-only.html), see [LICENSE.txt](https://github.com/matnoel/EasyFEA/blob/main/LICENSE.txt) and [CREDITS.md](https://github.com/matnoel/EasyFEA/blob/main/CREDITS.md) for more information.

## 💻  Installation

EasyFEA can be easily installed from [PyPI](https://pypi.org/project/EasyFEA/) using pip, compatible with Python versions 3.9 through 3.13:

```
pip install EasyFEA
```

You can also install EasyFEA with the [source code](https://github.com/matnoel/EasyFEA) using the `pip install .` command in the downloaded or cloned EasyFEA `folder`.

### 📦 Dependencies

EasyFEA uses several libraries, such as NumPy and Gmsh - as such, the following projects are required dependencies of EasyFEA:

+ [`numpy`](https://pypi.org/project/numpy/) - Fundamental package for scientific computing with Python.
+ [`gmsh`](https://pypi.org/project/gmsh/) (>= 4.12) - Three-dimensional finite element mesh generator.
+ [`scipy`](https://pypi.org/project/scipy/) - Fundamental package for scientific computing in Python.

### 🧪 Optional Dependencies

EasyFEA includes optional dependencies to reduce resolution time, plot results, or perform DIC:

+ [`matplotlib`](https://pypi.org/project/matplotlib/) - Plotting package.
+ [`pyvista`](https://pypi.org/project/pyvista/) - Plotting package.
+ [`pypardiso`](https://pypi.org/project/pypardiso/) (Python > 3.8 & Intel oneAPI)  - Library for solving large systems of sparse linear equations.
+ [`petsc`](https://pypi.org/project/petsc/) and [`petsc4py`](https://pypi.org/project/petsc4py/) - Python bindings for PETSc.
+ [`imageio`](https://pypi.org/project/imageio/) and [`imageio-ffmpeg`](https://pypi.org/project/imageio-ffmpeg/) - Library for reading and writing a wide range of image, video, scientific, and volumetric data formats.
+ [`meshio`](https://github.com/matnoel/meshio/tree/medit_higher_order_elements) - I/O for many mesh formats.
+ [`opencv-python`](https://pypi.org/project/opencv-python/) - Computer Vision package.
+ [`pygltflib`](https://pypi.org/project/pygltflib/) - Python library for reading, writing and managing 3D objects in the Khronos Group gltf and gltf2 formats.
+ [`usd-core`](https://pypi.org/project/usd-core/) - Pixar's Universal Scene Description.

## 🔤 Naming conventions

**EasyFEA** uses Object-Oriented Programming ([OOP](https://en.wikipedia.org/wiki/Object-oriented_programming)) with the following naming conventions:
+ `PascalCasing` for classes
+ `camelCasing` for properties
+ `Snake_Casing` or `Snake_casing` for functions/methods

In this library, objects can contain both **public** and **private** properties or functions.

**Private** parameters or functions are designated by a double underscore, such as `__privateParam`. In addition, parameters or functions beginning with an underscore, such as `_My_Function` are accessible to advanced users, but should be used with caution.

## ✍️ Citing EasyFEA

If you are using EasyFEA as part of your scientific research, please contribute to the scientific visibility of the project by citing it as follows.

> Noel M., *EasyFEA: a user-friendly Python library that simplifies finite element analysis*, https://hal.science/hal-04571962

Bibtex:

```
@softwareversion{noel:hal-04571962v1,
  TITLE = {{EasyFEA: a user-friendly Python library that simplifies finite element analysis}},
  AUTHOR = {Noel, Matthieu},
  URL = {https://hal.science/hal-04571962},
  NOTE = {},
  INSTITUTION = {{Universit{\'e} Gustave Eiffel}},
  YEAR = {2024},
  MONTH = Apr,
  SWHID = {swh:1:dir:ffb0e56fe2ce8a344ed27df7baf8f5f1b58700b5;origin=https://github.com/matnoel/EasyFEA;visit=swh:1:snp:88527adbdb363d97ebaee858943a02d98fc5c23c;anchor=swh:1:rev:ee2a09258bfd7fd60886ad9334b0893f4989cf35},
  REPOSITORY = {https://github.com/matnoel/EasyFEA},
  LICENSE = {GNU General Public License v3.0},
  KEYWORDS = {Finite element analyses ; Computational Mechanics ; Numerical Simulation ; Phase field modeling of brittle fracture ; Linear elasticity ; Euler-Bernoulli beam ; DIC - Digital Image Correlation ; User friendly ; Object oriented programming ; Mesh Generation},
  HAL_ID = {hal-04571962},
  HAL_VERSION = {v1},
}
```

## 📘 Projects and Publications

### 📝 Scientific Publications

- Noel M. et al.,  *Parameter identification for phase-field modeling of brittle fracture in spruce wood* - Engineering Fracture Mechanics, https://doi.org/10.1016/j.engfracmech.2025.111304

### 🧪 Research Projects

- [Material parameters of a phase-field model used to simulate brittle fracture of spruce specimens.](https://gitlab.univ-eiffel.fr/collaboration-msme-fcba/spruce-params)
- [Stochastic phase-field modeling of spruce wood specimens under compression.](https://gitlab.univ-eiffel.fr/collaboration-msme-fcba/spruce-stochastic)

## 🤝 Contributing

**EasyFEA** is an emerging project with a strong commitment to growth and improvement. Your input and ideas are invaluable to me. I welcome your comments and advice with open arms, encouraging a culture of respect and kindness in our collaborative journey towards improvement.

To learn more about contributing to EasyFEA, please consult the [Contributing Guide](https://github.com/matnoel/EasyFEA/blob/main/CONTRIBUTING.md).

# Contents

```{eval-rst}
.. toctree::
    :maxdepth: 1

    gallery/index
    begin
    howto/index
    examples/index
    api/index
```

# Indices and tables

```{eval-rst}
* :ref:`genindex`
* :ref:`modindex`
* :ref:`search`
```