On the significance of asperity models predictions of rough contact with respect to recent alternative theories

Abstract: Recently, it has been shown that while asperity models show correctly qualitative features of rough contact problems (linearity in area-load, negative exponential dependence of load on separation which means also linearity of stiffness with load), the exact value of the coefficients are not precise for the idealized case of Gaussian distribution of heigths. This is due to the intrinsic simplifications, neglecting asperity coalescence and interaction effects. However, the issue of Gaussianity has not been proved or experimentally verified in many cases, and here we show that, for example, assuming a Weibull distribution of asperity heigths, the area-load linear coefficient is not much affected, while the relationships load-separation and therefore also stiffness-load do change largely, particularly when considering bounded distributions of asperity heigths. It is suggested that Gaussianity of surfaces should be further tested in experiments, before applying the most sophisticated rough contact models based on the Gaussian assumption.