A Convex Route to Thermomechanics: Learning Internal Energy and Dissipation
This work addresses the challenge of thermodynamically consistent modeling in materials science, particularly for soft tissues and rubbers, by introducing a novel neural network approach that embeds physical principles, though it is incremental in its application to specific domains without internal variables.
The paper tackles the problem of discovering constitutive models in fully coupled thermomechanics by proposing a physics-based neural network framework that uses internal energy and dissipation potential as primary functions, avoiding mixed convexity-concavity conditions and ensuring thermodynamic admissibility. The results show that the learned models accurately capture constitutive behavior, as demonstrated on synthetic and experimental datasets including soft tissues and filled rubbers, with all code and data made publicly available.
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.