Open finite element infrastructure for nonlinear computational mechanics.
FElupe is an open, Python-based finite element infrastructure for nonlinear computational solid mechanics, providing high-level and extensible workflows for research and engineering applications.
✨ Highlights
- ✅ 100% Python package built with NumPy and SciPy
- ✅ easy to learn and productive high-level API
- ✅ nonlinear deformation of solid bodies
- ✅ interactive views on meshes, fields and solid bodies (using PyVista)
- ✅ typical finite elements
- ✅ cartesian, axisymmetric, plane strain and mixed fields
- ✅ hyperelastic material models with automatic differentiation
FElupe achieves efficient NumPy-based computations through vectorized element-wise operations on trailing array axes [1]. The finite element method, as used in FElupe, is based on [2], [3] and [4]. Related scientific articles are listed in the sections of the API reference.
[!NOTE] The name FElupe combines FE (finite element) with the German word Lupe (magnifying glass), highlighting the project's open and transparent approach to finite element simulation.
📦 Installation
Install Python, open a terminal and run
pip install felupe[all]
The documentation covers more details, like required and optional dependencies and how to install the latest development version.
🚀 Getting Started
This minimal code-block demonstrates a nonlinear simulation of a hyperelastic cube under compression.
import felupe as fem
mesh = fem.Cube(n=8)
region = fem.RegionHexahedron(mesh)
field = fem.FieldContainer(fields=[fem.Field(region, dim=3)])
boundaries = fem.dof.uniaxial(field, clamped=True, move=-0.3, return_loadcase=False)
solid = fem.SolidBody(umat=fem.NeoHooke(mu=1, bulk=5), field=field)
step = fem.Step(items=[solid], boundaries=boundaries)
job = fem.Job(steps=[step]).evaluate()
solid.plot("Principal Values of Cauchy Stress").show()
📖 Documentation
The documentation is located here.
🧩 Extension Packages
The capabilities of FElupe may be enhanced with extension packages created by the community.
| Package | Description |
|---|---|
| contique | Numerical continuation of nonlinear equilibrium equations. |
| hyperelastic | Constitutive hyperelastic material formulations |
| matadi | Material Definition with Automatic Differentiation (AD) |
| statescale | Snapshot-Driven State Upscaling |
| tensortrax | Differentiable Tensors based on NumPy Arrays |
| feplot | A visualization tool for FElupe |
🛠️ Testing
To run the FElupe unit tests, check out this repository and type
tox
📝 Scientific Publications
A list of articles in which
Expand the list...
-
A. Dutzler, C. Buzzi, and M. Leitner, "Nondimensional translational characteristics of elastomer components", Journal of Applied Engineering Design and Simulation, vol. 1, no. 1. UiTM Press, Universiti Teknologi MARA, Sep. 21, 2021. doi: 10.24191/jaeds.v1i1.20.
-
C. Buzzi, A. Dutzler, T. Faethe, J. Lassacher, M. Leitner, and F.-J. Weber, "Development of a tool for estimating the characteristic curves of rubber-metal parts", in Proceedings of the 12th International Conference on Railway Bogies and Running Gears, 2022 (ISBN 978-963-9058-46-0).
-
J. Torggler, A. Dutzler, B. Oberdorfer, T. Faethe, H. Müller, C. Buzzi, and M. Leitner, "Investigating Damage Mechanisms in Cord-Rubber Composite Air Spring Bellows of Rail Vehicles and Representative Specimen Design", Applied Composite Materials. Springer Science and Business Media LLC, Aug. 22, 2023. doi: 10.1007/s10443-023-10157-1. Simulation-related Python scripts are available on GitHub at adtzlr/fiberreinforcedrubber.
-
E. Navas, K. Blanco, D. Rodríguez-Nieto, and R. Fernández, "Design and grasp planning of a reconfigurable hybrid soft gripper using SINDy and virtual object representation", Sensors and Actuators A: Physical, vol. 401, p. 117621, Apr. 2026, doi: 10.1016/j.sna.2026.117621.
📄 Changelog
All notable changes to this project will be documented in this file. The format is based on Keep a Changelog, and this project adheres to Semantic Versioning.
📚 References
[1] T. Gustafsson and G. McBain, "scikit-fem: A Python package for finite element assembly", Journal of Open Source Software, vol. 5, no. 52. The Open Journal, p. 2369, Aug. 21, 2020. 
[2] J. Bonet and R. D. Wood, "Nonlinear Continuum Mechanics for Finite Element Analysis". Cambridge University Press, Mar. 13, 2008. 
[3] K. J. Bathe, "Finite Element Procedures". 2006, isbn: 978-0-9790049-0-2.
[4] O. C. Zienkiewicz, R. L. Taylor and J. Z. Zhu, "The Finite Element Method: its Basis and Fundamentals". Elsevier, 2013. 
🔓 License
FElupe - finite element analysis (C) 2021-2026 Andreas Dutzler, Graz (Austria).
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see https://www.gnu.org/licenses/.
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Release files for felupe 11.0.0
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Source distribution (sdist)
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| felupe-11.0.0-py3-none-any.whl | Python 3 | none | any | Details |
Total release size: 740.8 kB
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