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.

Polymers find widespread applications in various industries, such as civil engineering, aerospace, and industrial machinery, contributing to vibration control, dampening, and insulation. To accurately design products that are able to predict their dynamic behavior in the virtual environment, it is essential to understand and reproduce their viscoelastic properties via material physical modeling. While Dynamic Mechanical Analysis (DMA) has traditionally been used, innovative non-destructive techniques are emerging for characterizing components and monitoring their performance without deconstructing them. In this context, the Time–Temperature Superposition Principle (TTSP) represents a powerful empirical procedure to extend a polymer’s viscoelastic behavior across a wider frequency range. This study focuses on replicating an indentation test on viscoelastic materials using the non-destructive Viscoelasticity Evaluation System evolved (VESevo) tool. The primary objective is to derive a unique temperature–frequency relationship, referred to as a “shift law”, using characteristic curves from this non-invasive approach. Encouragingly, modifying the device setup enabled us to replicate, virtually, three tests under identical initial conditions but with varying indentation frequencies. This highlights the tool’s ability to conduct material testing across a range of frequencies. These findings set the stage for our upcoming experiment campaign, aiming to create an innovative shift algorithm from at least three distinct master curves at specific frequencies, offering a significant breakthrough in non-destructive polymer characterization with broad industrial potential.

Tire wear arises from coupled viscoelastic deformation, interfacial friction, temperature, and material fatigue, with growing relevance for performance, durability, and environmental impact. This review synthesizes the main families of tire-wear models, including empirical, analytical, numerical, and data-driven approaches, and examines their physical assumptions, predictive range, computational cost, and applicability to realistic tire road conditions. Emphasis is placed on friction and wear interactions, rubber specific complexities, and the absence of a common tribological framework. This work offers three key contributions: a systematic classification of modeling approaches and their assumptions; integration of environmental and regulatory drivers relevant to tire wear assessment; and an evaluation of model applicability across validation contexts, from laboratory tests to indoor rigs and real world conditions. Remaining challenges include transient dynamics, thermo-mechanical coupling, and model generalization. Future directions highlight the need for physically grounded and efficient models able to bridge scales, materials, and applications.