Friction for a sliding adhesive viscoelastic cylinder: Effect of Maugis parameter

We solve numerically the problem of a sliding viscoelastic cylinder in the presence of adhesion, modelled using the Lennard Jones force-separation law. For the material, a linear standard viscoelastic model is considered. We show the entire problem, and the friction coefficient in particular, depends on four dimensionless quantities: the Maugis–Tabor parameter λ, the dimensionless load W, the dimensionless speed V, and the ratio between the relaxed and the instantaneous modulus of the material, k=E0/E∞. For small λ, which corresponds to small rather rigid cylinders, friction returns to the classical Hunter solution for large compressive loads. For intermediate and large λ adhesion plays a significant role, and the “JKR limit” shows an adhesive component of the friction force which reaches the limit of the surface adhesion times the ratio of instantaneous to relaxed moduli at some intermediate speeds. The results obtained are in qualitative agreement with reported experimental results and can serve to guide the comparison with experiments, where it is known that the role of adhesion in rubber friction is still largely unclear and treated very often with semi-empirical equations