On the Significance of Asperity Models Predictions of Rough Contact with Respect to Recent Alternative Theories

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 heights. 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 heights, 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 heights. It is suggested that Gaussianity of surfaces should be further tested in the experiments, before applying the most sophisticated rough contact models based on the Gaussian assumption.