Hysteretic friction in elastomer-rough surface contacts: A continuum mechanics approach without empirical parameters

Abstract

Friction in viscoelastic contacts with rough rigid surfaces is commonly described using phenomenological laws or semi-empirical models, which limit predictive capability outside calibrated conditions. In this article, we present a continuum mechanics framework capable of predicting viscoelastic friction coefficients without prescribing empirical friction laws or adjustable parameters. The friction coefficient emerges naturally from the contact interaction between a deformable elastomer and a rigid rough surface, driven by the interplay between surface geometry, material rheology, and the geometric nonlinearity inherent to finite deformations. A two-dimensional model was implemented in COMSOL Multiphysics® using the finite element method. The viscoelastic constitutive response was described by a finite-strain formulation combining Neo-Hookean hyperelasticity with viscous dissipation, expressed in terms of the second Piola–Kirchhoff stress tensor. This nonlinear framework captures the large local deformations that occur at asperity contacts, which play a critical role in the energy dissipation mechanism underlying hysteretic friction. The experimentally measured surface topography, obtained via confocal microscopy, and the frequency-dependent rheological parameters of nitrile butadiene rubber (NBR), determined through dynamic mechanical analysis, were directly incorporated into the formulation. Friction coefficients were evaluated from both simulations and tribometric tests under controlled sliding velocities (0.25–5 mm/s) and normal pressures (5–50 kPa). The results show quantitative agreement between predicted and measured values, capturing the velocity-dependent hysteresis mechanism, the characteristic Grosch-like bell-shaped friction curve, and the saturation of contact area with increasing normal pressure. This approach establishes a robust connection between continuum-mechanics-based modeling and tribological experiments, paving the way toward a numerical tribometer capable of predicting frictional responses of elastomers against real rough surfaces across a wide variety of contact conditions.