Hetero-EUCLID

Wed, 30 Sep 2026 00:00:00 +0000

Hetero-EUCLID segments a heterogeneous specimen into its material regions and discovers an interpretable hyperelastic model for each region, using only full-field displacements and boundary reaction forces, without stress data. It builds on Bayesian-EUCLID and works in two steps: residual force-based segmentation, then constitutive parameter identification with a sparsity-promoting spike-and-slab prior sampled by MCMC.

The repository includes example FE datasets (cross-shaped inclusion and split domain) for reproducing the results in the paper.

Quick start

git clone https://github.com/d3lab-iisc/Hetero-EUCLID.git
cd Hetero-EUCLID
pip install -r requirements.txt
cd drivers
python main_hss_hetero_euclid.py Type1_Cross_Shaped_Inclusion none

See the repository README for the conda environment, noise levels and output files.

Citation

If you use this code, please cite the paper:

K. L. Chaurasiya, S. Dutta, S. Kumar, A. Joshi. Hetero-EUCLID: Interpretable model discovery for heterogeneous hyperelastic materials using stress-unsupervised learning. Computer Methods in Applied Mechanics and Engineering, 452, 118729 (2026). doi:10.1016/j.cma.2026.118729

To cite the software itself, use the archived release on Zenodo: 10.5281/zenodo.23359467.

Bayesian-EUCLID

Wed, 22 Jun 2022 00:00:00 +0000

Bayesian-EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) discovers interpretable hyperelastic material models, with quantified uncertainties, from full-field displacement data and reaction forces, without stress data. A large library of constitutive features is combined with sparsity-promoting spike-and-slab priors, and the physics-constrained likelihood is based on linear momentum balance. Gibbs sampling then gives parsimonious models as posterior distributions with epistemic and aleatoric uncertainties.

Compared to the earlier EUCLID framework, it discovers material models about 100 times faster while using far less data. The repository includes the quasi-static and dynamic FE benchmark data used in the paper (Arruda-Boyce, Gent-Thomas, Haines-Wilson, Holzapfel, Isihara, Neo-Hookean, Ogden).

Quick start

git clone https://github.com/EUCLID-code/EUCLID-hyperelasticity-bayesian.git
cd EUCLID-hyperelasticity-bayesian/drivers
python main_hss.py ArrudaBoyce high

Requires Python with numpy, scipy, torch, pandas, matplotlib, seaborn and scikit-learn. See the online documentation for a file-by-file explanation and a worked example, and the EUCLID project website for related codes.

Citation

If you use this code, please cite the paper:

A. Joshi, P. Thakolkaran, Y. Zheng, M. Escande, M. Flaschel, L. De Lorenzis, S. Kumar. Bayesian-EUCLID: Discovering hyperelastic material laws with uncertainties. Computer Methods in Applied Mechanics and Engineering, 398, 115225 (2022). doi:10.1016/j.cma.2022.115225

Typo corrections to the published article are listed here.

Python | Dynamics Data Design Lab

Hetero-EUCLID

Quick start

Citation

Bayesian-EUCLID

Quick start

Citation