A novel multiscale model for contact behavior analysis of rough surfaces with the statistical approach

This paper presents a contact model to describe the normal and tangential contact behaviors of the rough interface with multiscale topographies. The coupling effect of macroscopic profile deviation and mesoscopic roughness on the contact behaviors is taken into account. First, an improved force expression of single contacting asperity is proposed to characterize the continuous and monotonic feature in the whole deformation process. By adopting the statistical summation, the contact model for the surface with microscopic topography is established. Second, the mesoscopic waviness deformation is characterized with microscopic asperities through multiscale modeling. The macroscopic geometric deviation is defined as a linear shape function. By combining the macro-, meso-- and microscopic topographies, the multiscale normal contact model is established. Then, in terms of tangential model, the Jenkins element is applied to express the slip-stick behavior of asperity. Based on the normal contact model and Coulomb law, the distribution function of the yield slip force is obtained to establish the tangential contact model. Furthermore, the predicted contact responses are compared with experiments and finite element model to validate the effectiveness of the proposed model. Finally, the influences of the multiscale topographies are analyzed, presenting the variation tendencies of contact responses. This work provides a feasible and effective way for studying the contact response of rough interface with multiscale surface topographies.