Frictional Contacts Between Rough Grains With Fractal Morphology

Abstract Surface morphology plays a crucial role in friction between two contacting geomaterial surfaces, yet many questions remain unanswered regarding how detailed frictional responses deviate from analytical solutions for smooth surfaces due to the presence of roughness. In this study, we revisit the Cattaneo‐Mindlin problem for contacts between two fractally rough elastic or elasto‐plastic spheres generated based on ultra‐high degree (e.g., up to 2,000) spherical harmonics with the corresponding wavelength less than a thousandth of the mean grain diameter. Transverse contacts are simulated by finite element method, validated by the extended Cattaneo‐Mindlin solution to full slide regime for smooth sphere contacts. Extensive simulations are conducted to study contacts between two rough spheres with various surface geometries, micro friction coefficients, normal contact distances, relative roughness, fractal dimensions, and wavelength ranges. Out results indicate that: (a) the new analytical solution can approximately predict the macro contact response except for extremely high relative roughness and narrow wavelength range; (b) deviations induced by roughness from smooth sphere contacts can be neutralized by plasticity, high normal contact interference, and high micro friction coefficient; and (c) fractal dimension impacts frictional contacts less than relative roughness. The main cause of these phenomena can be credited to the underlying microscale contact information. Contact area and stress distributions and their evolutions provide concrete evidence of these observed behavior. This work provides a pathway for applying computational contact mechanics to many geophysical fields, such as the asperity model in earthquake science and the mechanics of granular materials.