Update README.md (#850)

* Update README.md * Update README.md * Update README.md
adtzlr · Sep 5, 2024 · 6bf9b33 · 6bf9b33
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 [![FElupe](https://img.shields.io/badge/%F0%9F%94%8D-FElupe-white)](https://felupe.readthedocs.io) [![PyPI version shields.io](https://img.shields.io/pypi/v/felupe.svg)](https://pypi.python.org/pypi/felupe/) [![Documentation Status](https://readthedocs.org/projects/felupe/badge/?version=latest)](https://felupe.readthedocs.io/en/latest/?badge=latest) [![License: GPL v3](https://img.shields.io/badge/License-GPLv3-blue.svg)](https://www.gnu.org/licenses/gpl-3.0) [![codecov](https://codecov.io/gh/adtzlr/felupe/branch/main/graph/badge.svg?token=J2QP6Y6LVH)](https://codecov.io/gh/adtzlr/felupe) [![DOI](https://zenodo.org/badge/360657894.svg)](https://zenodo.org/badge/latestdoi/360657894) ![Codestyle black](https://img.shields.io/badge/code%20style-black-black) ![PyPI - Downloads](https://img.shields.io/pypi/dm/felupe) [![lite-badge](https://jupyterlite.rtfd.io/en/latest/_static/badge.svg)](https://adtzlr.github.io/felupe-web/lab?path=01_Getting-Started.ipynb) <a target="_blank" href="https://colab.research.google.com/github/adtzlr/felupe-web/blob/main/notebooks/colab/01_Getting-Started.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a>
 
-FElupe is a Python 3.8+ 🐍 finite element analysis package 📦 focusing on the formulation and numerical solution of nonlinear problems in continuum mechanics 🔧 of solid bodies 🚂. Its name is a combination of FE (finite element) and the german word *Lupe* 🔍 (magnifying glass) as a synonym for getting an insight 📖 how a finite element analysis code 🧮 looks like under the hood 🕳️.
+FElupe is a Python 3.8+ 🐍 finite element analysis package 📦 focusing on the formulation and numerical solution of nonlinear problems in continuum mechanics 🔧 of solid bodies 🪨. This package is intended for scientific research 💻, but is also suitable for running nonlinear simulations 🚂 in general 🏎️. In addition to the transformation of general weak forms into sparse vectors and matrices, as also available in [[1]](https://doi.org/10.21105/joss.02369), FElupe provides an efficient high-level abstraction layer for the simulation of the deformation of solid bodies.
 
 <p align="center">
   <a href="https://felupe.readthedocs.io/en/latest/examples/ex01_beam.html"><img src="https://felupe.readthedocs.io/en/latest/_images/sphx_glr_ex01_beam_thumb.png" height="100px"/></a> <a href="https://felupe.readthedocs.io/en/latest/examples/ex02_plate-with-hole.html"><img src="https://felupe.readthedocs.io/en/latest/_images/sphx_glr_ex02_plate-with-hole_thumb.png" height="100px"/></a> <a
@@ -29,6 +29,21 @@ FElupe is a Python 3.8+ 🐍 finite element analysis package 📦 focusing on th
   href="https://felupe.readthedocs.io/en/latest/examples/ex20_third-medium-contact.html"><img src="https://felupe.readthedocs.io/en/latest/_images/sphx_glr_ex20_third-medium-contact_thumb.png" height="100px"/></a>
 </p>
 
+# Highlights
+- [x] 100% Python package built with [NumPy](https://numpy.org/) and [SciPy](https://scipy.org/)
+- [x] easy to learn and productive high-level [API](https://felupe.readthedocs.io/en/latest/felupe.html)
+- [x] nonlinear deformation of [solid bodies](https://felupe.readthedocs.io/en/latest/felupe/mechanics.html#felupe.SolidBody)
+- [x] interactive views on meshes, fields and solid bodies (using [PyVista](https://pyvista.org/))
+- [x] typical [finite elements](https://felupe.readthedocs.io/en/latest/felupe/element.html)
+- [x] axisymmetric, plane strain and mixed fields
+- [x] [hyperelastic material models](https://felupe.readthedocs.io/en/latest/felupe/constitution/hyperelasticity.html)
+- [x] strain energy density functions with [automatic differentiation](https://felupe.readthedocs.io/en/latest/felupe/constitution/hyperelasticity.html#felupe.Hyperelastic)
+
+The concept of efficient math-operations in [NumPy](https://numpy.org/) with elementwise operating *trailing axes* is inspired by [[1]](https://doi.org/10.21105/joss.02369). The finite element method, as used in FElupe, is based on [[2]](https://doi.org/10.1017/cbo9780511755446), [[3]]() and [[4]](https://doi.org/10.1016/c2009-0-24909-9). Related scientific articles are listed in the sections of the [API reference](https://felupe.readthedocs.io/en/latest/felupe.html).
+
+> [!NOTE]
+> *FElupe* is a combination of FE (finite element) and the german word *Lupe* 🔍 (magnifying glass) as a synonym for getting an insight 📖 how a finite element analysis code 🧮 looks like under the hood 🕳️.
+
 # Installation
 Install Python, fire up 🔥 a terminal and run 🏃
 
@@ -116,17 +131,26 @@ tox
 # Scientific Publications
 A list of articles in which [![FElupe](https://img.shields.io/badge/%F0%9F%94%8D-FElupe-white)](https://felupe.readthedocs.io) is involved. If you use FElupe in your scientific work, please star this repository, cite it [![DOI](https://zenodo.org/badge/360657894.svg)](https://zenodo.org/badge/latestdoi/360657894) and add your publication to this list.
 
-1. A. Dutzler, C. Buzzi, and M. Leitner, "Nondimensional translational characteristics of elastomer components", [Journal of Applied Engineering Design and Simulation](https://jaeds.uitm.edu.my/index.php/jaeds), vol. 1, no. 1. UiTM Press, Universiti Teknologi MARA, Sep. 21, 2021. doi: [10.24191/jaeds.v1i1.20](https://doi.org/10.24191/jaeds.v1i1.20). [![medium-story](https://img.shields.io/badge/medium-story-white)](https://medium.com/@adtzlr/nonlinear-force-displacement-curves-of-rubber-metal-parts-ab7c48448e96)
+- A. Dutzler, C. Buzzi, and M. Leitner, "Nondimensional translational characteristics of elastomer components", [Journal of Applied Engineering Design and Simulation](https://jaeds.uitm.edu.my/index.php/jaeds), vol. 1, no. 1. UiTM Press, Universiti Teknologi MARA, Sep. 21, 2021. doi: [10.24191/jaeds.v1i1.20](https://doi.org/10.24191/jaeds.v1i1.20). [![medium-story](https://img.shields.io/badge/medium-story-white)](https://medium.com/@adtzlr/nonlinear-force-displacement-curves-of-rubber-metal-parts-ab7c48448e96)
 
-2. C. Buzzi, A. Dutzler, T. Faethe, J. Lassacher, M. Leitner, and F.-J. Weber, "Development of a tool for estimating 
+- 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](https://transportation.bme.hu/2022/11/30/bogie22/), 2022 (ISBN 978-963-9058-46-0).
 
-3. 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](https://www.springer.com/journal/10443). Springer Science and Business Media LLC, Aug. 22, 2023. doi: [10.1007/s10443-023-10157-1](https://link.springer.com/article/10.1007/s10443-023-10157-1). Simulation-related Python scripts are available on GitHub at [adtzlr/fiberreinforcedrubber](https://github.com/adtzlr/fiberreinforcedrubber). <a target="_blank" href="https://colab.research.google.com/github/adtzlr/fiberreinforcedrubber/blob/main/docs/notebooks/ex01_specimen_amplitudes.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a>
+- 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](https://www.springer.com/journal/10443). Springer Science and Business Media LLC, Aug. 22, 2023. doi: [10.1007/s10443-023-10157-1](https://link.springer.com/article/10.1007/s10443-023-10157-1). Simulation-related Python scripts are available on GitHub at [adtzlr/fiberreinforcedrubber](https://github.com/adtzlr/fiberreinforcedrubber). <a target="_blank" href="https://colab.research.google.com/github/adtzlr/fiberreinforcedrubber/blob/main/docs/notebooks/ex01_specimen_amplitudes.ipynb"><img src="https://colab.research.google.com/assets/colab-badge.svg" alt="Open In Colab"/></a>
 
 # Changelog
 All notable changes to this project will be documented in [this file](CHANGELOG.md). The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/), and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+# References
+[[1]](https://doi.org/10.21105/joss.02369) T. Gustafsson and G. McBain, "*[scikit-fem](https://github.com/kinnala/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. [![DOI:10.21105/joss.02369](https://zenodo.org/badge/DOI/10.21105/joss.02369.svg)](https://doi.org/10.21105/joss.02369).
+
+[[2]](https://doi.org/10.1017/cbo9780511755446) J. Bonet and R. D. Wood, "*Nonlinear Continuum Mechanics for Finite Element Analysis*". Cambridge University Press, Mar. 13, 2008. [![DOI:10.1017/cbo9780511755446](https://zenodo.org/badge/DOI/10.1017/cbo9780511755446.svg)](https://doi.org/10.1017/cbo9780511755446).
+
+[[3]]() K. J. Bathe, "*Finite Element Procedures*". 2006, isbn: 978-0-9790049-0-2.
+
+[[4]](https://doi.org/10.1016/c2009-0-24909-9) O. C. Zienkiewicz, R. L. Taylor and J. Z. Zhu, "The Finite Element Method: its Basis and Fundamentals". Elsevier, 2013. [![DOI:10.1016/c2009-0-24909-9](https://zenodo.org/badge/DOI/10.1016/c2009-0-24909-9.svg)](https://doi.org/10.1016/c2009-0-24909-9).
+
 # License
 FElupe - finite element analysis (C) 2021-2024 Andreas Dutzler, Graz (Austria).