A Comprehensive Review of Rubber Contact Mechanics and Friction Theories

This review surveys theoretical frameworks developed to describe rubber contact and friction on rough surfaces, with a particular focus on tire–road interaction. It begins with classical continuum approaches, which provide valuable foundations but show limitations when applied to viscoelastic materials and multiscale roughness. More recent formulations are then examined, including the Klüppel–Heinrich model, which couples fractal surface descriptions with viscoelastic dissipation, and Persson’s theory, which applies a statistical mechanics perspective and later integrates flash temperature effects. Grosch’s pioneering experimental work is also revisited as a key empirical reference linking friction, velocity, and temperature. A comparative discussion highlights the ability of these models to capture scale-dependent contact and energy dissipation while also noting practical challenges such as calibration requirements, parameter sensitivity, and computational costs. Persistent issues include the definition of cutoff criteria for roughness spectra, the treatment of adhesion under realistic operating conditions, and the translation of detailed power spectral density (PSD) data into usable inputs for predictive models. The review emphasizes progress in connecting material rheology, surface characterization, and operating conditions but also underscores the gap between theoretical predictions and real tire–road performance. Bridging this gap will require hybrid approaches that combine physics-based and data-driven methods, supported by advances in surface metrology, in situ friction measurements, and machine learning. Overall, the paper provides a critical synthesis of current models and outlines future directions toward more predictive and application-oriented tire–road friction modeling.