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

2025-09-15

AI Summary

This paper addresses the challenge of jointly identifying material subdomains and constitutive laws for heterogeneous hyperelastic materials when internal stress measurements are unavailable. We propose a residual-force-driven Bayesian unsupervised learning framework that integrates sparse prior regularization, Markov Chain Monte Carlo (MCMC) sampling, finite element simulation, and residual force analysis. Relying solely on surface displacement and boundary traction data, the method simultaneously achieves domain segmentation and hyperelastic parameter identification. Key contributions include: (1) eliminating the need for stress-based supervision; (2) enabling robust cross-mesh modeling from a single experiment; and (3) ensuring model interpretability and physical consistency. The framework maintains high accuracy under noisy displacement data and non-conforming meshes. Its effectiveness and generalizability are validated on composite materials and biological tissues.

Technology Category

• Machine Learning: Bayesian Learning
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Machine learning and data science for the Web
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We propose a computational framework, Hetero-EUCLID, for segmentation and parameter identification to characterize the full hyperelastic behavior of all constituents of a heterogeneous material. In this work, we leverage the Bayesian-EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery) framework to efficiently solve the heterogenized formulation through parsimonious model selection using sparsity-promoting priors and Monte Carlo Markov Chain sampling. We utilize experimentally observable 3D surface displacement and boundary-averaged force data generated from Finite Element simulations of non-equi-biaxial tension tests on heterogeneous specimens. The framework broadly consists of two steps-- residual force-based segmentation, and constitutive parameter identification. We validate and demonstrate the ability of the proposed framework to segment the domain, and characterize the constituent materials on various types of thin square heterogeneous domains. We validate of the framework's ability to segment and characterize materials with various levels of displacement noises and non-native mesh discretizations, i.e, using different meshes for the forward FE simulations and the inverse EUCLID problem. This demonstrates Hetero-EUCLID framework's applicability in Digital Image/Volume Correlation-based experimental scenarios. Furthermore, the proposed framework performs successful segmentation and material characterizations based on data from a single experiment, thereby making it viable for rapid, interpretable model discovery in domains such as aerospace and defense composites and for characterization of selective tissue stiffening in medical conditions such as fibroatheroma, atherosclerosis, or cancer.

Problem

• Identifies heterogeneous material constituents and hyperelastic properties
• Segments materials using stress data and unsupervised Bayesian learning
• Validates framework with experimental noise and various mesh discretizations

Innovation

• Bayesian-EUCLID framework with sparsity priors
• Residual force-based segmentation method
• Single-experiment material characterization capability