Cycle-domain plasticity modeling using neural networks and symbolic regression

Journal article, 2026

Simulation of many loading cycles with traditional time-domain material models, requiring discretization of each cycle with several time steps, can result in high computational cost. One effective approach to speed up cyclic simulations is employing cycle-domain material models. Finite element simulations of rails subjected to many wheel passages are a relevant application of such models. Proposing a per-cycle evolution equation for plastic strains in cycle-domain models is, however, a challenge. To address this, we investigate the feasibility and accuracy of using machine learning models as tools for formulating such an equation. Specifically, we enforce our knowledge from constitutive modeling for elasticity and formulate the evolution law by employing feed-forward neural networks with different inputs, as well as symbolic regression to discover an interpretable expression. Training, validation, and test data have been generated using a cyclic time-domain plasticity model considering pulsating uniaxial stress loadings with constant and variable strain ranges. The obtained results demonstrate the potential of cycle-domain plasticity modeling using both uninterpretable and interpretable data-driven machine learning as an alternative to time-domain material modeling. Furthermore, both approaches have revealed reasonably good extrapolation performance beyond the training regime.