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 procedure, 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.

The accurate prediction of tire and brake thermomechanical behavior is crucial for various applications in the automotive industry, including vehicle dynamics analysis, racing performance optimization, and driver assistance system development. The temperature of the brakes plays a crucial role in determining the performance of rubber by altering its temperature. This change impacts the rim and the air within the tire, leading to variations in temperature and tire pressure, which consequently affect the vehicle’s overall performance. Traditionally, these components have been modeled separately, neglecting the crucial thermal interaction between them, thereby losing a lot of important information from the outside that influences the tire. This paper presents a novel method that overcomes this limitation by coupling the thermomechanical models of the tire and brake, enabling a more comprehensive understanding of their combined behavior. Therefore, the present work could be an interesting starting point to understand how a control system can be influenced by the thermodynamic of the wheel–brake system.