Computational results and Python files for the work "A four-field mixed formulation for incompressible finite elasticity"

This repository contains the code and data accompanying the paper "A four-field mixed formulation for incompressible finite elasticity".

The implementation is based on the open-source Finite Element library NGSolve (www.ngsolve.org). To generate the data, we used NGSolve-version NGSolve-6.2.2406-131-ged00b3bce.

The implementation of the NDTNS, CSMFEM, Simo-Taylor-Pister (STP)-like, and Taylor-Hood-like methods for incompressible finite elasticity can be found in ndtns.py, csmfem.py, stp.py, and standard.py, respectively.

In newton_raphson.py, the (quasi-)Newton-Raphson method is implemented, and several options are set in general_options.py. To count the methods' degrees of freedom, we used dof_counting.py.

The data for the numerical experiments is generated by running

cylinder2D.py, cylinder3D.py, cook2D.py, cook3D.py, and block3D.py.

The generated raw data (.pkl) and tables (.csv and .tex) are stored in the data.zip folder.

For the post-pressing, we used compute_mix_max_determinants.py to compute the violation of the incompressibility constraint and visualize.py to generate the pictures of the solutions.