A Theoretical Study on Friction of Macroscale Patterned Surfaces: Implications for Scaling Up Superlubricity.

"Structural superlubricity", a state of frictionless sliding between crystalline surfaces, has been observed at the nanoscale and microscale. However, achieving it at the macroscale requires further investigation. Inspired by recent experimental studies, we theoretically examine the friction behavior of macroscale patterned surfaces composed of microscale bumps coated with superlubricious two-dimensional materials. We performed numerical simulations with the discrete element method. The Hertz contact model, along with a modified tangential Mindlin contact model, is employed to capture the nonlinear relationship between the coefficient of friction and normal load. Our results reveal that the friction behavior is significantly influenced by the radius of the microscale bumps, the durability of the coating, and the elasticity of the surface, and we show how those can be tuned to improve friction properties. Additionally, we analytically investigate the deformation mechanisms of the surface structure and derive scaling laws for parameters and the breakdown of superlubricity. The simulation results show strong agreement with the analytical derivations of power laws for scaling of various quantities with the total macroscopic load. Finally, we examine imperfect conditions by investigating how height variations impact frictional performance.