Nonlinear mathematical modeling of frequency-temperature dependent viscoelastic materials for tire applications

Understanding and accurately reproducing the realistic response of rubber materials to external stimuli is a crucial research topic that involves all the engineering fields and beyond where these materials are used. This study introduces an innovative nonlinear fractional derivative generalized Maxwell model designed to effectively capture and replicate the experimental behavior of viscoelastic materials. The proposed model addresses the limitations observed in conventional fractional models, providing greater versatility which makes it more suitable for describing the intricate behavior of polymeric materials. Through rigorous mathematical validation, the proposed model demonstrates coherence with the underlying physics of the viscoelastic behavior. To address the identification pro- cedure, the pole-zero formulation is adopted, employing a multi-objective optimization to obtain the optimum, able to replicate the dynamic moduli trends. Satisfying results have been validated over a wide dataset of 10 different materials, demonstrating an extended capability of adapting to different variations than classical widely-used fractional models. Furthermore, the model has proven to be valid even employing a reduced amount of experimental data limited only to low, high- frequency plateaus and around the glass transition temperature, which could be fundamental for optimizing resources in experimental investigations.