CANN-EUCLID: unsupervised constitutive artificial neural network model discovery from full-field data

2026-06-12

AI Summary

This work addresses the challenge of robustly identifying multidimensional constitutive relationships for soft biological tissues from a single non-uniform loading experiment, which traditional constitutive artificial neural networks struggle with due to their reliance on homogeneous stress–strain data. By integrating the Constitutive Artificial Neural Network (CANN) framework with EUCLID, the proposed method enables stress-free supervised discovery of hyperelastic constitutive laws using only full-field displacements and boundary reaction forces—without requiring local stress measurements or assuming a predefined constitutive form. The approach minimizes finite element equilibrium residuals augmented with sparsity-promoting regularization, accurately recovering complex constitutive expressions involving exponential terms. Benchmark tests on isotropic and anisotropic materials demonstrate faithful reconstruction of ground-truth constitutive terms, and forward finite element simulations confirm high-fidelity reproduction of mechanical responses, with extrapolation accuracy contingent upon whether the training loads sufficiently excite the relevant deformation mechanisms.

Abstract

Constitutive artificial neural networks (CANNs) provide interpretable material model discovery, but have so far been used in stress-supervised settings based on apparent stress-strain data from homogeneous tests. Because each test samples only a narrow loading path and provides homogenized rather than local stress information, robust discovery typically requires multiple loading modes to constrain the multidimensional response. This is challenging for soft biological tissues, where repeated testing, damage, and sample variability limit reliable information from a single specimen. Here, we combine CANNs with the stress-unsupervised full-field discovery framework EUCLID to identify sparse hyperelastic laws directly from displacement fields and reaction forces in one heterogeneity-inducing loading case. CANN-EUCLID minimizes equilibrium imbalance with sparsity-promoting regularization selecting compact active terms, without local stress measurements or a prescribed law. We evaluate the approach on isotropic and anisotropic benchmarks with prescribed ground-truth laws. When the ground truth is representable by the chosen CANN basis, our method recovers the correct terms with near-exact accuracy, including exponential terms with embedded parameters. When it is not contained in the basis, the method retains shared terms and approximates missing contributions using available basis functions. Generalization depends strongly on sampled deformation states: exponential strain-stiffening terms can be recovered accurately when sufficiently probed, but can produce large extrapolation errors when the stiffening regime lies outside the sampled domain. Forward FE validation simulations show that the discovered behavior accurately replicates the ground truth. These results establish stress-unsupervised CANN discovery as a promising framework for interpretable full-field constitutive model identification.

Problem

• constitutive model discovery
• unsupervised learning
• full-field data
• soft biological tissues
• hyperelasticity

Innovation

• Constitutive Artificial Neural Networks
• Unsupervised Discovery
• Full-field Data
• Sparse Hyperelasticity
• EUCLID