Holthusen H, Steinmann P, Kuhl E (2026)
Publication Type: Journal article
Publication year: 2026
Book Volume: 459
Article Number: 119082
DOI: 10.1016/j.cma.2026.119082
We present a physics-based neural network framework for the discovery of constitutive models in fully coupled thermoelasticity. 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 proposed unsupervised learning strategy is directly applied to full-field data, with the constitutive potentials embedded into the discretized balance laws. During training, an auxiliary entropy network is employed to predict the entropy from the observable deformation and temperature fields, while the implicit entropy relation is recovered by an iterative solver during inference. The results show that the learned models accurately capture the underlying constitutive behavior. All code, data, and trained models are made publicly available via Zenodo.org.
APA:
Holthusen, H., Steinmann, P., & Kuhl, E. (2026). A convex route to thermoelasticity: Learning internal energy and dissipation. Computer Methods in Applied Mechanics and Engineering, 459. https://doi.org/10.1016/j.cma.2026.119082
MLA:
Holthusen, Hagen, Paul Steinmann, and Ellen Kuhl. "A convex route to thermoelasticity: Learning internal energy and dissipation." Computer Methods in Applied Mechanics and Engineering 459 (2026).
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