Elastic Contact Mechanics of Randomly Rough Surfaces: An Assessment of Advanced Asperity Models and Persson's Theory

In this work, we discuss important improvements of asperity models. Specifically, we assess the predictive capabilities of a recently developed multiasperity model, which differs from the original Greenwood and Williamson model by (i) including the coupling between the elastic fields generated by each contact spot, and (ii) taking into account the coalescence among the contact areas, occurring during the loading process. Interaction of the elastic field is captured by summing the contributions, which are analytically known, of the elastic displacements in a given point of the surface due to each Hertzian-like contact spot. The coalescence is instead considered by defining an equivalent contact spot in such a way to guarantee conservation of contact area during coalescence. To evaluate the accuracy of the model, a comparison with fully numerical 'exact' calculations and Persson's contact mechanics theory of elastic rough surfaces is proposed. Results in terms of contact area versus load and separation versus load show that the three approaches give almost the same predictions, while traditional asperity models neglecting coalescence and elastic coupling between contact regions are unable to correctly capture the contact behavior. Finally, very good results are also obtained when dealing with the probability distribution of interfacial stresses and gaps.