Multiscale modeling of rubber friction

The main component of rubber friction on rough substrates, such as in the case of a car tire on a road surface, is of hysteretic nature, i.e. it is due to viscoelastic energy dissipation taking place in the bulk of the material. 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. Our 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.