In soft-materials friction, the roughness of rigid countersurfaces plays a significant role, since it affects the amplitude and frequency of internal strain. This study analyzes steady sliding friction between a planar Kelvin-Voigt viscoelastic foundation and a nominally flat rigid plate with periodic asperities under two constraint conditions imposed on the rigid plate: position- and force-controlled. Although previous studies using a single-asperity model have revealed that only the latter condition exhibits bell-shaped velocity-dependent friction, numerical simulations of the present multiple-asperity model show bell-shaped friction even under the former condition. The model’s simplicity analytically yields the complete set of dimensionless numbers and the asymptotic solutions. Conclusively, we find two crucial roles of surface roughness: the stationary contact state and the deformation history. The former explains why we cannot obtain a single master curve for the present model. The latter provides a different mechanism for the bell-shaped friction than the single-asperity model.
