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Although considerable attention has been devoted to the development of models for isother- mal, rate-independent plasticity, many high-consequence performance assessments involve vis- coplastic processes that generate substantial heat. In addition, materials may transit from a nearly isothermal, rate-independent regime to a viscous, temperature-dependent regime during these processes, which makes modeling more challenging. In this work, we develop a physics- augmented neural network (PANN) framework for modeling general temperature-dependent, rate-dependent inelastic processes firmly based on physical principles, including the second law of thermodynamics and coordinate equivariance. These embedded properties are enabled by a number of architectural innovations in the structure and training of an input convex and potential- based neural ordinary differential equation (NODE) framework, including an adaptively rectified dissipation potential and joint observable-hidden invariants. The resulting neural network mod- els are capable of representing a wide spectrum of rate- and temperature-dependence ranging from isothermal, rate-independent elastic-plastic phenomenology to rate-dependent fully viscous inelastic behavior, as we demonstrate. Although the demonstrations are based on isotropic in- variants, the formulation is directly extensible to anisotropy given a suitable set of invariants. We also show that the framework is capable of modeling complex microstructural inelasticity and predicting the conversion of plastic work to heating when calibrated to stress-temperature observations.
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This content will become publicly available on March 3, 2027
A hierarchy of thermodynamics learning frameworks for inelastic constitutive modeling
Recent advances in physics-augmented neural networks have enabled thermodynamically consistent data-driven constitutive modeling of complex inelastic materials. Most existing approaches, however, implicitly adopt a specific thermodynamic framework and embed structural assumptions such as normality, dual dissipation potentials, or other structure from manually constructed models directly into the learning architecture. Consequently, differences in predictive performance may arise not only from data or network design, but also from the underlying theoretical assumptions. In this work, we present a unified comparison of several thermodynamically consistent inelastic modeling frameworks from a machine learning perspective. We consider internal-variable formulations with dissipation potential, generalized standard materials, and metriplectic structures, and we analyze their structural assumptions, admissible dependencies, convexity requirements, and implications for dissipation and evolution. Each framework is implemented within a common neural potential architecture based on invariant representations and neural ordinary differential equations. This unified setting ensures that performance differences can be attributed to thermodynamic structure rather than architectural variation. The models are trained and evaluated on three representative inelastic datasets generated from high-fidelity representative volume element simulations: an elastoplastic alloy, a viscoelastic composite, and a rate-dependent crystal plasticity polycrystal. By isolating the role of thermodynamic structure, we assess how restrictions such as duality, normality, operator-based evolution, and convexity influence learnability, expressiveness, stability, and generalization.
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- Award ID(s):
- 2452029
- PAR ID:
- 10682209
- Publisher / Repository:
- arXiv: https://arxiv.org/pdf/2603.02645
- Date Published:
- Format(s):
- Medium: X
- Institution:
- The University of Texas at Austin
- Sponsoring Org:
- National Science Foundation
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