Numerical analysis on the adhesive contact between a rigid power-law shaped axisymmetric asperity and an elastic half-space

There exist many well-known analytical models for adhesive contact for spherical asperities. However, in many situations, the asperities are not spherical and may be better described by a power-law function. Thus, these well-known analytical models were extended to power-law-shaped axisymmetric asperities in the past decades. In this paper, numerical simulation is employed for the adhesive contact between a rigid power-law axisymmetric asperity and an elastic half-space. The realistic Lennard-Jones potential and the Derjaguin approximation are used for the surface traction. Numerical simulations are performed with different shape indexes and different Tabor parameters. The whole solution is obtained. Semi-empirical formulas for the pull-off forces, the contact radius at zero loads, the jump-in distance, and the pull-off distance are proposed. All these equations are both simple and as accurate as of the numerical simulations.