Mechanistic model for contact between rough surfaces

Interactions at interfaces play a pivotal role in the mechanics of particulate and fractured material. This paper focusses on the mathematical modeling of force-deformation behavior of interface between two rough surfaces. A mechanistic approach is adopted wherein the overall behavior of rough interfaces are considered via interaction of asperities on the interface. The interacting asperities are modeled using the Hertz-Mindlin contact theory. Both elastic deformation and frictional sliding are accounted at asperity contacts. The topography of the interface is represented via statistical distributions of asperity contact orientations, asperity heights, and asperity curvature. A modified spherical harmonic expansion is introduced to model the asperity contact orientation distribution. The resulting interface force-deformation model is used to predict the normal and the shear stiffness of rough interfaces. The model is verified via comparison with experimental data culled from the literature.