A Convex Route to Thermomechanics: Learning Internal Energy and Dissipation

2026-03-30

AI Summary

This work addresses the challenge that conventional thermomechanical constitutive models often fail to satisfy mixed convex-concave conditions and struggle to consistently embed fundamental thermodynamic principles. To overcome this, the authors propose a physics-informed neural network framework grounded in internal energy and dissipation potential. Taking deformation and entropy as state variables, the method indirectly infers entropy via temperature, enabling thermodynamically consistent modeling without requiring ground-truth entropy data. Innovatively integrating input convex neural networks (ICNNs), invariant representations, and a zero-anchor strategy, the architecture intrinsically enforces the second law of thermodynamics, objectivity, material symmetry, and normalization priors. The approach accurately reproduces both purely thermal and fully coupled thermomechanical responses of soft tissues and filled rubber on synthetic and experimental datasets, with code made publicly available.

Abstract

We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermomechanics. In contrast to classical formulations based on the Helmholtz energy, we adopt the internal energy and a dissipation potential as primary constitutive functions, expressed in terms of deformation and entropy. This choice avoids the need to enforce mixed convexity--concavity conditions and facilitates a consistent incorporation of thermodynamic principles. In this contribution, we focus on materials without preferred directions or internal variables. While the formulation is posed in terms of entropy, the temperature is treated as the independent observable, and the entropy is inferred internally through the constitutive relation, enabling thermodynamically consistent modeling without requiring entropy data. Thermodynamic admissibility of the networks is guaranteed by construction. The internal energy and dissipation potential are represented by input convex neural networks, ensuring convexity and compliance with the second law. Objectivity, material symmetry, and normalization are embedded directly into the architecture through invariant-based representations and zero-anchored formulations. We demonstrate the performance of the proposed framework on synthetic and experimental datasets, including purely thermal problems and fully coupled thermomechanical responses of soft tissues and filled rubbers. The results show that the learned models accurately capture the underlying constitutive behavior. All code, data, and trained models are made publicly available via https://doi.org/10.5281/zenodo.19248596.

Problem

• thermomechanics
• constitutive modeling
• internal energy
• dissipation potential
• thermodynamic consistency

Innovation

• input convex neural networks
• thermomechanics
• constitutive modeling
• internal energy
• dissipation potential