Learning inelastic constitutive models from stress-strain data under hard thermodynamic constraints

Abstract

Machine learning approaches informed by physics have offered new insights into the discovery of constitutive models from data, helping overcome some limitations of traditional constitutive modelling while reducing the cost of otherwise computationally intensive simulations. Yet, many existing methods either enforce only part of the relevant physical and thermodynamic structure, or achieve thermodynamic consistency within specific constitutive classes, leaving open questions about their applicability across a broad range of material behaviours and their ability to generalise to unseen loading paths when limited data are available. This work establishes a thermodynamics-constrained learning framework for inelastic constitutive models from macroscopic stress-strain data. The framework is based on non-equilibrium thermodynamics and parameterises both the free energy and the generalised transport operator governing the evolution of the material state, while enforcing material objectivity, energy balance, and non-negative dissipation as hard, scalable constraints. Analytical benchmarks involving simple stress-strain loading paths demonstrate that the method learns thermodynamically consistent and robust constitutive models for a range of inelastic materials of increasing complexity. At inference, the resulting models generalise to more demanding, unobserved paths and identify interpretable internal variables that capture path-dependent behaviours. The framework is then applied to granular media, prototypical heterogeneous and history-dependent materials. Trained on numerically simulated experiments based on the discrete element method, the method identifies admissible constitutive equations and predicts the response under cyclic loading, including the emergence of hysteresis absent from the training data, relying solely on macroscopic stress-strain histories.

References in corpus (18)

• On dense granular flows
• Thermodynamics-based Artificial Neural Networks for constitutive modeling
• A new family of Constitutive Artificial Neural Networks towards automated model discovery
• Multiscale modeling of inelastic materials with Thermodynamics-based Artificial Neural Networks (TANN)
• Neural networks meet hyperelasticity: A guide to enforcing physics
• Granular Solid Hydrodynamics
• Automated discovery of generalized standard material models with EUCLID
• Deep learning of thermodynamics-aware reduced-order models from data
• Theory and implementation of inelastic Constitutive Artificial Neural Networks
• Variational Onsager Neural Networks (VONNs): A thermodynamics-based variational learning strategy for non-equilibrium PDEs
• Evolution TANN and the identification of internal variables and evolution equations in solid mechanics
• Geometric deep learning for computational mechanics Part II: Graph embedding for interpretable multiscale plasticity
• Applying GSH to a Wide Range of Experiments in Granular Media
• Neural integration for constitutive equations using small data
• Dissipation-consistent modelling and classification of extended plasticity formulations
• Data-driven methods for computational mechanics: A fair comparison between neural networks based and model-free approaches
• Microinertia and internal variables
• Hydrodynamics of fault gouges from constitutive modelling to the physics of friction