compmec / hyper

Solve static non-linear mechanics problems using Finite Elements Method for hyperelastic materials

Non-linear-mechanics

Introduction

This repository contains the code used in the cours HYPER(Numerical Methods for NonLinear Mechanics) at the École Centrale de Nantes.

Subject

The non-linear mechanics is used when the hypothesis of small deformations is not valid. For exemple, we have the images below that shows when it's applied a big force in the center.

The main difference between the approachs are:

• Linear mechanics
  • Integration doesn't consider the deformed space
  • Eulerien's description
  • Cauchy's strain tensor
• Non-linear mechanics
  • Integration considers the deformed space
  • Lagrangian's description
  • Green-Lagrangian's strain tensor

Coding and librarys

For implementation, we use Python with the libraries:

• Numpy: Used for tensor calculs
• Gmsh: Used to get the mesh and elements

To use the codes, you just need these packages and the python installed. The easiest way to do it is using the Anaconda that installs everything you need.

Documentation

All documentation is kept in our wiki, with usage and examples.

Authors

• Carlos Adir Ely Murussi Leite
• Clément Fuchs