CANNs

When using, please cite "A new family of Constitutive Artificial Neural Networks towards automated model discovery", CMAME, https://doi.org/10.1016/j.cma.2022.115731 as well as the relevant other papers provided by this repository.

All input data and code is provided in the corresponding folders.

Abaqus

Universal material modeling subroutine, simulation input files, and benchmark simulations.

1. General framework - "A universal material model subroutine for soft matter systems", https://doi.org/10.1007/s00366-024-02031-w
2. Orthotropic hyperelastic material behavior; myocardial tissue, "Automated model discovery for human cardiac tissue: discovering the best model and parameters", https://doi.org/10.1016/j.cma.2024.117078
3. Transverse isotropic material behavior; arterial tissue, "Democratizing biomedical simulation through automated model discovery and a universal material subroutine", https://doi.org/10.1007/s00466-024-02515-y
4. Isotropic hyperelastic material behavior; brain tissue, "On automated model discovery and a universal material subroutine", https://doi.org/10.1016/j.cma.2023.116534

ArtMeat

Models and data for animal and plant-based meat papers.

1. Valanis-Landel type, principal-stretch-based, and invariant-based models, "Discovering the mechanics of artificial and real meat" https://doi.org/10.1016/j.cma.2023.116236

   Revision summary: we have corrected two coding mistakes that had small effects on Table 4, Figures 8, 9, 10, 11, and the text starting on page 18 bottom; the revised code, updated table, figures, and text are all in this GitHub folder; the main findings of this study are not affected by these updates.

2. Invariant-based model, "The mechanical and sensory signature of plant-based and animal meat" https://doi.org/10.1101/2024.04.25.591207

3. Invariant-based model, "Biaxial testing and sensory texture evaluation of plant-based and animal meat" https://www.biorxiv.org/content/10.1101/2025.02.19.639170v1

BCANN

Bayesian constitutive artifical neural network, "Discovering uncertainty: Bayesian constitutive artificial neural networks" https://doi.org/10.1101/2024.08.19.608595

Brain

Isotropic models and data for brain papers.

1. Invariant-based model, "Automated model discovery for human brain using Constitutive Artificial Neural Networks" https://doi.org/10.1016/j.actbio.2023.01.055
2. Principal-stretch-based model and invariant model, " Principal-stretch-based constitutive neural networks autonomously discover a subclass of Ogden models for human brain tissue" https://doi.org/10.1016/j.brain.2023.100066

Heart

Orthotropic model and shear and biaxial data for heart papers.

1. "Automated model discovery for human cardiac tissue: Discovering the best model and parameters" https://doi.org/10.1016/j.cma.2024.117078
2. "Discovering dispersion: How robust is automated model discovery for human myocardial tissue?" https://doi.org/10.1007/s10237-025-02005-x

Muscle

Viscoelastic constitutive recurrent neural network model, "Automated model discovery for muscle using constitutive recurrent neural networks" https://doi.org/10.1016/j.jmbbm.2023.106021

Rubber

Isotropic invariant-based model, "A new family of Constitutive Artificial Neural Networks towards automated model discovery" https://doi.org/10.1016/j.cma.2022.115731

Skin

Anistropic constitutive artificial neural network model, "Automated model discovery for skin: Discovering the best model, data, and experiment" https://doi.org/10.1016/j.cma.2023.116007

Mesh

Knitted material anisotropic constitutive neural network, "Automated model discovery for textile structures: The unique mechanical signature of warp knitted fabrics" https://doi.org/10.1101/2024.07.26.605392

GCANN

Gaussian Constitutive Neural Network, "Discovering uncertainty: Gaussian constitutive neural networks with correlated weights." https://doi.org/10.48550/arXiv.2503.12679

GICANN

Generalized-invariant-based constitutive neural network, "Generalized invariants meet constitutive neural networks: A novel framework for hyperelastic materials." https://doi.org/10.1016/j.jmps.2025.106352

WORKSHOPS

Code, slides, and data from the Graz Summer Biomechanics School in 2023 and the ESB conference short course in 2025. Contains Google Colab code to run the same models and data as contained in the BRAIN folder.