Adhesive impact of an elastic sphere with an elastic half space: Numerical analysis based on the method of dimensionality reduction

• A fast numerical procedure for simulation of adhesive impacts is described and applied for simulation of impact of spherical particles.
• It is shown that the solution of the impact problem is completely determined by a two functions of two dimensionless parameters: the Mindlin ratio of the normal and tangential stiffness and one single parameter describing adhesion.
• Both determining functions have been found numerically in the complete relevant range of all relevant parameters.
• Based on numerical data, an analytic approximation has been found giving a “closed form solution” of the problem.

An impact of an elastic sphere with an elastic half space in the presence of adhesion is studied numerically using the method of dimensionality reduction. It is shown that the rebound velocities and angular velocity, written in proper dimensionless variables, are determined by a function of only the ratio of tangential and normal stiffness (“Mindlin-ratio”) and one further parameter describing the adhesion properties of the contact. The obtained numerical results can be approximated by analytical expressions.