This is a companion source code for the publication Simulating Hyperelasticity and Fractional Viscoelasticity in the Human Heart (DOI: 10.1016/j.cma.2023.116048).

This repository contains the following:

• Matlab caputo fractional derivative example (/matlab_example)
• Python caputo fractional derivative implementation (/src/py/caputoD)
• C++ caputo fractional derivative implementation (/src/cpp/fractional/caputo.cpp)
• Cython headers and module for compiling the c++ code to a python shared library (/src/cython)
• Script for generating the analytical solution in Example 1 of paper (compute_analytical_solutions.py)
• Script for generating the validation data for convergence with the number of Prony series (prony_serie_test.py)
• Script for generating the validation data for convergence with the scaling the time interval (time_interval_test.py)

The necessary python modules are listed in requirements.txt To compile the cython module, you can:

• Call Makefile (Linux only)
• Run python3 make.py
• Manually run pip install on requirements.txt and build /src/setup.py

Unit tests are available as examples and to test that the shared library is working properly

• Call make test
• Call python3 make.py test

The mittag-loeffler function is the fork of the repository by Konrad Hinsen, see

https://github.com/khinsen/mittag-leffler

@article{ZHANG2023simulating, title = {Simulating hyperelasticity and fractional viscoelasticity in the human heart}, journal = {Computer Methods in Applied Mechanics and Engineering}, volume = {411}, pages = {116048}, year = {2023}, issn = {0045-7825}, doi = {https://doi.org/10.1016/j.cma.2023.116048}, url = {https://www.sciencedirect.com/science/article/pii/S004578252300172X}, author = {Will Zhang and Javiera Jilberto and Gerhard Sommer and Michael S. Sacks and Gerhard A. Holzapfel and David A. Nordsletten}, keywords = {Viscoelasticity, Cardiac biomechanics, Cardiac modeling, Computational modeling, fractional viscoelasticity}, }