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🧭 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. Linear elastic simulations: static, dynamic, homogenization and mesh optimization.
  2. Hyperelastic simulations: static and dynamic in the Lagrangian framework..
  3. Inelastic simulations: small-strain plasticity, viscoplasticity and viscoelasticity, assembled from a yield surface, hardening, a back-stress, a rate law and Maxwell branches.
  4. Cardiac elasto-dynamics: passive + active hyperelastic mono-ventricular left-ventricle benchmark.
  5. Contact simulations: frictionless penalty contact against a rigid obstacle
  6. Euler-Bernoulli and Timoshenko beam simulations: static and dynamic.
  7. Thermal simulations: static and transient.
  8. Phase-field damage simulations for quasi-static brittle fracture: advanced 2D and 3D simulations for isotropic, transversely isotropic, and anisotropic materials.
  9. Weak forms simulations: static and dynamic for linear or non-linear problems.
  10. Digital Image Correlation (DIC) analyses.
  11. Parameter identification.
  12. Stochastic phase-field simulations.

📸 Explore the interactive gallery to visualize simulation results.

For each simulation, users create a mesh and a model. Once the simulation has been set up, defining the boundary conditions, solving the problem, and visualizing the results are straightforward.

Numerous examples of mesh creation are available in the Meshes gallery.

The simplest and quickest introduction is shown below and is available in the Beginner’s Guide.

import matplotlib.pyplot as plt

from EasyFEA import Matplotlib, ElemType, Models, Simulations
from EasyFEA.Geoms import Domain

# ----------------------------------------------
# Mesh
# ----------------------------------------------
L = 120  # mm
h = 13

domain = Domain((0, 0), (L, h), h / 3)
mesh = domain.Mesh_2D([], ElemType.QUAD9, isOrganised=True)

# ----------------------------------------------
# Simulation
# ----------------------------------------------
E = 210000  # MPa
v = 0.3
F = -800  # N

mat = Models.Elastic.Isotropic(2, E, v, planeStress=True, thickness=h)

simu = Simulations.Elastic(mesh, mat)

nodesX0 = mesh.Nodes_Conditions(lambda x, y, z: x == 0)
nodesXL = mesh.Nodes_Conditions(lambda x, y, z: x == L)

simu.add_dirichlet(nodesX0, [0, 0], ["x", "y"])
simu.add_surfLoad(nodesXL, [F / h / h], ["y"])

simu.Solve()

# ----------------------------------------------
# Results
# ----------------------------------------------
Matplotlib.Plot_Mesh(simu, deformFactor=10)
Matplotlib.Plot_BoundaryConditions(simu)
Matplotlib.Plot(simu, "uy", plotMesh=True)
Matplotlib.Plot(simu, "Svm", plotMesh=True, ncolors=11)

plt.show()

⚖️ 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, see LICENSE.txt and CREDITS.md for more information.

📚 Documentation

Refer to the documentation for detailed installation and usage details.

💻 Installation

EasyFEA can be easily installed from PyPI using pip, compatible with Python versions 3.9 through 3.13:

pip install EasyFEA

You can also install EasyFEA with the source code 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 - Fundamental package for scientific computing with Python.
  • gmsh (>= 4.12) - Three-dimensional finite element mesh generator.
  • scipy - Fundamental package for scientific computing in Python.

🧪 Optional Dependencies

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

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

🔤 Naming conventions

EasyFEA uses Object-Oriented Programming (OOP) 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

🧪 Research Projects

🤝 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.

Project links

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Avatar for matnoel from gravatar.com matnoel

Credits

Author: Matthieu Noel

License

GNU General Public License v3 (GPLv3) (GNU GENERAL PUBLIC LICENSE Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc...)

Requires

Python >=3.9

Provides Extra

dev io jax viz

Tags

finite-element-analysis phase-field python easy fem

Classifiers

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