Two Origins for Bell-Shaped Velocity-Dependent Friction Coefficient: Kelvin-Voigt or Standard Linear Solid Viscoelasticity

Abstract

It is well known that the friction coefficient of viscoelastic solids against the drive speed exhibits a bell shape. In previous theoretical studies on viscoelastic friction, we can find two origins for the bell shape. One is due to the material response (i.e., the bell-shaped rheology of viscoelastic solids), and the other is due to the mechanical response (i.e., the vertical lift of the counter surface with asperities). Although these two origins do not contradict each other, their relationship seems unclear. This paper theoretically examines the friction coefficient for the steady sliding contact between a rigid probe and a viscoelastic foundation exhibiting the standard linear solid viscoelasticity. Capitalizing on the strength of the simple model, we successfully find the complete set of dimensionless numbers and master curves describing the velocity dependence of the friction coefficient. Comparing them with the dimensionless numbers and master curves for the Kelvin-Voigt viscoelasticity, we clarify two origins for the bell-shaped velocity-dependent friction coefficient and their relationship.