Discovering plasticity models without stress data

Abstract

We propose a new approach for data-driven automated discovery of material laws, which we call EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery), and we apply it here to the discovery of plasticity models, including arbitrarily shaped yield surfaces and isotropic and/or kinematic hardening laws. The approach is unsupervised, i.e., it requires no stress data but only full-field displacement and global force data; it delivers interpretable models, i.e., models that are embodied by parsimonious mathematical expressions discovered through sparse regression of a potentially large catalogue of candidate functions; it is one-shot, i.e., discovery only needs one experiment. The material model library is constructed by expanding the yield function with a Fourier series, whereas isotropic and kinematic hardening are introduced by assuming a yield function dependency on internal history variables that evolve with the plastic deformation. For selecting the most relevant Fourier modes and identifying the hardening behavior, EUCLID employs physics knowledge, i.e., the optimization problem that governs the discovery enforces the equilibrium constraints in the bulk and at the loaded boundary of the domain. Sparsity promoting regularization is deployed to generate a set of solutions out of which a solution with low cost and high parsimony is automatically selected. Through virtual experiments, we demonstrate the ability of EUCLID to accurately discover several plastic yield surfaces and hardening mechanisms of different complexity.

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Cited by in corpus (25)

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• Modular machine learning-based elastoplasticity: generalization in the context of limited data
• Finite electro-elasticity with physics-augmented neural networks
• Automated identification of linear viscoelastic constitutive laws with EUCLID
• Automated discovery of interpretable hyperelastic material models for human brain tissue with EUCLID
• Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions
• Reduced and All-at-Once Approaches for Model Calibration and Discovery in Computational Solid Mechanics
• Can KAN CANs? Input-convex Kolmogorov-Arnold Networks (KANs) as hyperelastic constitutive artificial neural networks (CANs)
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• HyperCAN: Hypernetwork-Driven Deep Parameterized Constitutive Models for Metamaterials
• Integrated Digital Image Correlation for Micro-Mechanical Parameter Identification in Multiscale Experiments
• Single-test evaluation of directional elastic properties of anisotropic structured materials
• Automated Model Discovery for Tensional Homeostasis: Constitutive Machine Learning in Growth and Remodeling
• A topology optimisation framework to design test specimens for one-shot identification or discovery of material models
• A generalized dual potential for inelastic Constitutive Artificial Neural Networks: A JAX implementation at finite strains
• A Complement to Neural Networks for Anisotropic Inelasticity at Finite Strains
• COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates
• Unsupervised Material Fingerprinting: Ultra-fast hyperelastic model discovery from full-field experimental measurements
• Hetero-EUCLID: Interpretable model discovery for heterogeneous hyperelastic materials using stress-unsupervised learning
• Enhancing material behavior discovery using embedding-oriented Physically-Guided Neural Networks with Internal Variables
• Solving strategies for data-driven one-dimensional elasticity exhibiting nonlinear strains
• A physics-informed data-driven framework for modeling hyperelastic materials with progressive damage and failure