1D Stress Evolution Prediction via Thermodynamically-Informed Neural Networks

Abstract:

Accurate modeling of elastoplastic behavior is crucial for forming simulations, yet conventional constitutive laws require extensive calibration and often fail to generalize across diverse loading paths. To address this limitation, a thermodynamically informed neural-network framework is proposed for predicting one-dimensional stress evolution. The model integrates physical consistency into a data-driven formulation by coupling two neural components: one learns the state evolution, predicting increments of the internal variable, while the other approximates the Helmholtz free-energy potential, from which stresses are obtained via automatic differentiation. Synthetic datasets generated from randomized strain paths with power-law hardening were used for training, ensuring broad coverage of nonlinear responses. The model successfully reproduces monotonic, unloading, reverse, and random loading behaviors with minimal error accumulation and stable recursive inference. Owing to its incremental formulation, the framework maintains predictive accuracy beyond the trained strain range, offering a physically interpretable and data-efficient alternative to conventional constitutive models.

• Periodical: Solid State Phenomena (Volume 390)
• Pages: 51-61
• DOI: https://doi.org/10.4028/p-Vj1faR
• Online since: April 2026
• Authors: Alireza Fallahnejad*, Emin Semih Perdahcioglu, Ton van den Boogaard
• Keywords: Constitutive Modelling, Elastoplasticity, Machine Learning, Thermodynamic Consistency

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