adtzlr / hyperelastic

Constitutive hyperelastic material formulations for FElupe.

Hi there 🖐️,

this is Andreas, a mechanical engineer graduated from Graz University of Technology, based in 🏰⛰️ Graz, Austria 🇦🇹. In my free time, I like running 🏃‍, skiing ⛷️ and snowboarding 🏂 while I also enjoy family times at home 👨‍👩‍👧‍👦.

Currently, I'm an engineer in industry (during the day) and a PhD student at Graz University of Technology at the Institute of Structural Durability and Railway Technology (well, at night... 📚 🕯️). All the tools related to my scientific work are available here on my GitHub profile.

I'm the author of 🔍 FElupe, an open-source finite element analysis package focussing on the formulation and numerical solution of nonlinear problems in continuum mechanics of solid bodies. Most of the open source finite element packages I found are either super-difficult to install, needs to be compiled or are great but slow (or at least too slow for my needs).

With FElupe, I try to fill a gap in between.

I'm convinced that static input files 🖨️ which are passed to a standalone fea solver 🖩 are a thing of the last decades 💾. Instead, scripts are input files: easy to adopt scripts with access to third-party libraries 🛒, written in common scripting languages are the way to go. With common languages I mean something easy-to-learn for engineers, like Python, Matlab/Octave or Julia, not another proprietary simulation file format. FElupe is just another one of many open-source finite element analysis packages using this approach. Well defined and public available scripting interfaces hopefully accelerate the introduction of flexible natural language-processing for simulations.

Projects

• 🔧 Mechanics: felupe, hyperelastic, matadi, trusspy, contique, cubrium, fiberreinforcedrubber
• 🔢 Math: tensortrax, ttb, neinsum

Code Snippets

• 1D Finite Element Analysis in 100 Lines of Python Code
• 3D Finite Element Analysis in 100 Lines of Python Code
• 3D Finite Element Analysis in 100 Lines of Python Code (Alternative Assembly)
• 3D Hyperelastic Finite Element Analysis in 140 Lines of Python Code

hyperelastic's Issues

Bugs in Generalized Invariants

• typo in second invariant
• use more general expressions for the initial state and default exponent=2 in \hyperelastic\models\generalized\_stretch.py

`InvariantsFramework`: Add third invariant

Bug in Neo-Hookean material formulation from `ThirdOrderDeformation`

The out-argument of an einsum-call has wrong shape (is not broadcastable).

`ogden()`: Take a list of mu and alpha instead of scalars

Finish `GeneralizedInvariantsFramework`

with invariants based on the principal values of the Seth-Hill strain tensor.

Curve Fit: Find material parameters for given Experimental Data

This should be a simple wrapper for scipy.optimize.curve_fit().

Classes for hyperelastic.lab

• Experiment: Holds all the experiment-related data in attributes, e.g. displacement, force, time, temperature, cross-sectional area, label, etc. as well as methods for stress- and stetch-evaluations
• LoadCase: Base-class for pre-defined loadcases with methods for calculating the deformation gradient from the stretch and the (e.g. uniaxial) stress. In other words, the 1d-deformation (stretch) is converted to a 3d-deformation (gradient tensor) and the 3d stress tensor is converted back to a 1d stress related to the experiment.
• Simulation: Create a simulation on top of a loadcase with given stretches and evaluate the stress (also for the curve-fit of scipy). In the future, numeric simulations would be a great extension.
• Optimize: Combine experiments and simulations and find the set of parameters which give the best-fit to the experiments. Optimize.run() is then the wrapper of scipy.optimize.curve_fit().

Collection of Figures

Implement a native Lab

instead of taking it from matadi.