Hetero-EUCLID: Interpretable model discovery for heterogeneous hyperelastic materials using stress-free unsupervised learning

Computer Methods in Applied Mechanics and Engineering

🧠 Unsupervised model discovery without stress input — interpretable and automatic.

In this work, we developed Hetero-EUCLID, an interpretable model discovery framework designed to identify material behavior in heterogeneous hyperelastic structures, without using stress data. Instead, it works solely with full-field displacement and boundary force data, mimicking real-world Digital Image Correlation (DIC) experiments.

The method works in two stages: First, it locates material interfaces by analyzing where the internal force balance breaks down, using a clever combination of residual analysis and a random-seed-based clustering algorithm. This lets us segment the domain into regions of different material properties. Next, we solve for region-specific material models using a sparse, probabilistic approach that stitches everything together into a globally consistent heterogeneous model.

We tested Hetero-EUCLID across a variety of material layouts, mesh types, and noise levels—proving that it’s not just accurate, but also robust and experiment-friendly.