Influence of Periodic Asperities on Viscoelastic Friction in Planar Sliding Contact

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 singleasperity model.