ABSTRACT Accurate modeling of cyclic damage evolution is essential for predicting the long‐term performance and durability of engineering materials and structures. Traditional simulation‐based approaches, while physically rigorous, are computationally expensive, especially under complex loading histories. In this work, we present a physics‐based machine learning () framework that integrates physical laws into neural network architectures to efficiently and reliably model cyclic damage evolution. The approach leverages high‐fidelity data generated from one‐dimensional phase‐field simulations of brittle fracture under varying cyclic loading scenarios and material properties. The proposed architecture incorporates two coupled feed‐forward neural networks: one to predict the phase‐field damage variable and another to compute the free energy, both trained jointly using a loss function that enforces thermodynamic consistency, energy dissipation, and irreversibility of damage under cyclic loading. The model's performance is evaluated across interpolation and extrapolation scenarios, including unseen loading paths and material parameters. Compared to a purely data‐driven feed‐forward neural network, the model demonstrates significantly improved accuracy, robustness, and physical reliability, especially in predicting long, path‐dependent loading histories. These results underscore the importance of embedding physics into machine learning for modeling degradation processes and highlight the potential of hybrid models as efficient, interpretable surrogates for complex numerical simulations.
Elsayed et al. (Wed,) studied this question.