Asperity Interaction and Substrate Deformation in Statistical Summation Models of Contact Between Rough Surfaces

A method is proposed to account for asperity interaction and bulk substrate deformation in models that utilize statistical summation of asperity forces to characterize contact between rough surfaces. Interaction deformations of noncontacting asperities are calculated based on the probability that they have taller neighbors in their vicinity, whose deformation upon contact, in turn, induces local substrate deformations. The effect of the order of interaction on the total contact force is explored and a limit is proposed based on asperity density. The updated contact force accounting for asperity interaction is found to tend to a constant fraction of the nominal contact force at the mathematical limit of asperity contact independent of the order of interaction, roughness, or material properties. For contact in the vicinity of zero mean plane separation, rough surfaces are found to exhibit greater asperity interaction resulting in reduced contact forces. A simplified curve-fitted expression is introduced that can be used to account for asperity interaction by adjusting the nominal contact force predicted by other models.