The nonlinear dynamic behaviours and modelling of polymer elements in railway tracks: a state-of-the-art review

The continuous advancement of railways towards higher speeds and heavier axle loads has exacerbated the challenges of vibration and noise, particularly in environmentally sensitive areas. Polymer elements, such as rail pads, under sleeper pads, under ballast mats, and under slab mats, play a pivotal role in preserving track integrity and reducing environmental impact. However, their dynamic mechanical behaviour exhibits strong nonlinear dependencies on temperature, loading frequency, strain amplitude, and preload, which cannot be accurately captured by traditional linear Kelvin-Voigt models. This state-of-the-art review systematically synthesizes the latest research on the nonlinear dynamic behaviours and modelling of these polymer elements in railway tracks. It details the experimental evidence of their complex, multi-factor coupled nonlinear characteristics and elucidates the underlying mechanisms, including the Payne and Mullins effects. This paper provides a comprehensive analysis and comparison of various nonlinear dynamic models developed to overcome the limitations of the linear model, ranging from fractional derivative models to generalized Maxwell model and data-driven models. The review highlights the significant impact of incorporating these nonlinear models into vehicle-track coupled dynamics simulations, demonstrating their necessity for achieving accurate predictions of mid-to-high frequency dynamic responses. Moreover, the paper identifies key research gaps and future directions. This work provides a valuable reference for researchers and engineers aiming to enhance the precision of track dynamics analysis and optimize vibration mitigation strategies for sustainable railway development.