Dynamic Contact of a Rigid Sphere With an Elastic Half-Space: A Numerical Simulation

A numerical simulation is performed to investigate the development of forces between a rigid sphere and an elastic half-space during normal, dynamic contact in the absence of friction. Of interest is to quantify the magnitude of forces that arise and to identify any sources of hysteresis between approach and separation, the latter being associated with energy dissipation. In the simulation a rigid sphere approaches and separates from an isotropic, linearly elastic half-space at a prescribed, constant speed. Surface forces are incorporated in the model by ascribing a surface interaction potential derived from the Lennard-Jones 6-12 intermolecular potential. Dynamical equations of motion for the interface are integrated numerically during the approach-separation event. During the approach phase, it is found that the magnitude of adhesive force is generally consistent with well-known static-equilibrium based analytical models (e.g., DMT and JKR), depending upon the strength of the interaction potential. However, during separation, the attractive force computed in this dynamic simulation may be several times higher than the predictions of the analytical models. Additionally, the maximum compressive forces attained during the contact process far exceed the predictions of Hertzian contact theory. The discrepancy between results of this simulation and those of the static-equilibrium analytical and numerical models indicate that dynamic interactions play a significant role in determining the development of contact forces. Moreover, dynamic effects persist even when the approach-separation speed of the sphere is small compared to the dilatation and shear wave speeds of the half-space.