Abstract：Polymer materials have gained widespread application in aerospace, transportation, and industrial processing due to their excellent wear resistance, efficient energy absorption capabilities, and outstanding impact resistance. In these application scenarios, the mechanical behavior of these materials exhibits complex rate sensitivity and temperature dependence, especially under extreme high-speed impact loading. These nonlinear responses are critical factors for structural integrity. This poses significant challenges for constitutive modeling. In classical physical models, researchers mainly improve the performance of the models by modifying rubber elasticity models, optimizing thermally activated flow rules, or introducing network branching structures. However, these improvements rely on many undetermined coefficients, which makes specific parameter calibration quite difficult in practical engineering. As for classical phenomenological models, the model performance is mainly improved by modifying the hardening term and introducing new branches. Essentially, these methods enhance the model's ability to describe mechanical behavior by assigning it more undetermined coefficients, but this also leads to problems such as difficulties in parameter calibration. Machine learning methods provide a new research direction for constitutive modeling. These methods are superior to classical models in terms of prediction accuracy and generalization ability, and can significantly reduce experimental costs. Purely data-driven machine learning models rely entirely on data to capture the mechanical response of materials, and face problems such as large data requirements, possible violation of physical laws, and overfitting or underfitting. Therefore, scholars have proposed hybrid models that combine traditional constitutive theory with machine learning algorithms to overcome these limitations. Among them, physics-informed neural networks (PINNs) have shown particularly broad application prospects due to their unique ability to learn physical laws, and have become a current research hotspot. In summary, this review systematically elucidates the evolution and optimization strategies of polymer constitutive models, providing a theoretical foundation for developing next-generation models with both physical consistency and high predictive accuracy.
2026, Vol. 47 
