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

TL;DR

This paper introduces a thermodynamics-constrained machine learning framework that learns consistent and robust inelastic constitutive models from stress-strain data, capable of generalizing to unseen loading paths.

Contribution

It embeds non-equilibrium thermodynamics principles as hard constraints in a scalable learning architecture for constitutive modeling from macroscopic data.

Findings

Learns thermodynamically consistent models for complex inelastic materials.

Models generalize to unobserved loading paths and recover internal variables.

Successfully applied to granular media, capturing hysteresis from stress-strain histories.

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, most existing approaches only partially enforce the requirements of physics and thermodynamics, leaving open questions about their consistency across a broad range of material behaviours and their ability to generalise robustly to unseen loading paths when only limited measurements are available. This work establishes a thermodynamics-constrained learning framework whose architecture embeds the principles of non-equilibrium thermodynamics, objectivity and stability as hard, scalable constraints to learn constitutive models from standard macroscopic data. Analytical benchmarks involving 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 can autonomously recover interpretable internal variables that capture path-dependent evolution. The framework is then applied to granular media, prototypical heterogeneous and history-dependent materials for which constitutive modelling remains challenging. Trained on numerically simulated experiments based on the discrete element method, the model discovers the underlying constitutive equations and predicts responses under cyclic loading, including the emergence of hysteresis absent from the training data, relying solely on macroscopic stress-strain histories. The findings indicate that enforcing non-equilibrium thermodynamics through hard constraints represents a principled route to robust, consistent, and scalable data-driven discovery of constitutive models.