Computational homogenization of rubber friction on rough rigid surfaces

The main component of rubber friction is known to be of hysteretic nature, i.e. it is due to viscoelastic energy dissipation taking place in the bulk of the material as a result of the pulsating forces induced by the surface asperities whenever rubber slides on a rough substrate, such as in the case of a car tire on a road surface. This implies that the observed macroscopic friction depends upon the constitutive behavior of the rubber and the characteristics of the rough surface profile. In contrast to analytical models, numerical approaches can fully account for geometric and material non-linearities arising in the rubber behavior, especially at small scales. However, explicit numerical modeling of rough surface features spanning a wide range of significant length scales would result prohibitively expensive, which motivates the need for a computational multiscale framework. As shown by previous related research, fractal surface profiles can be decomposed into a finite number of sinusoidal terms, so that a central ingredient of a multiscale approach becomes the homogenization of rubber friction on a sinusoidal surface. This work proposes a computational homogenization procedure where a macroscale coefficient of friction for rubber is derived from the solution of a microscale boundary-value problem. The latter considers contact of a representative volume element (RVE) with a sinusoidal rigid surface, which is assumed to represent the smallest length scale of a fractal rough surface. The numerical model is developed within the isogeometric framework and features a mortar formulation for the unilateral contact problem in the discretized setting. Numerical aspects related to the choice of the RVE, the setup of the test parameters and the convergence rate of different discretizations are discussed. Physically relevant observations concern the role of the macroscopic applied pressure and sliding velocity on the homogenized friction coefficient. Some comparisons with analytical results as well as dimensional analysis considerations are further reported.