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

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.

References in corpus (20)

• Data-driven computational mechanics
• Model-Free Data-Driven Inelasticity
• A new family of Constitutive Artificial Neural Networks towards automated model discovery
• Unsupervised discovery of interpretable hyperelastic constitutive laws
• Geometric deep learning for computational mechanics Part I: Anisotropic Hyperelasticity
• Data-Driven Design for Metamaterials and Multiscale Systems: A Review
• Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy
• The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting
• Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)
• NN-EUCLID: deep-learning hyperelasticity without stress data
• Automated discovery of generalized standard material models with EUCLID
• Data-driven fracture mechanics
• Data driven problems in elasticity
• Discovering plasticity models without stress data
• Local approximate Gaussian process regression for data-driven constitutive laws: Development and comparison with neural networks
• Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs
• On spike-and-slab priors for Bayesian equation discovery of nonlinear dynamical systems via sparse linear regression
• Automated identification of linear viscoelastic constitutive laws with EUCLID
• On-the-fly construction of surrogate constitutive models for concurrent multiscale mechanical analysis through probabilistic machine learning
• Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energies