65Fundamentals of Friction
while further increasing the number of asperities, one can show that A
r
~ W.
Later, more sophisticated fractal surface models were introduced, which led
to similar results (Nosonovsky and Bhushan 2008).
Both statistical and fractal models of rough surfaces, for elastic and plastic
contact, combined with the adhesive friction law (Equation 4.5) result in an
almost linear dependency of the friction force upon the normal load in the
case of a small extent of contact (Figure4.4a).
4.2.1.5 Adhesion Hysteresis and Dissipation
The van der Waals adhesion force is conservative and, therefore, by itself
cannot provide a mechanism needed for energy dissipation. It was sug-
gested recently (Maeda et al. 2002; Szoszkiewicz et al. ...