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.