The Influence of Viscoelasticity on Velocity-Dependent Restitutions in the Oblique Impact of Spheres

We analyse the oblique impact of linear-viscoelastic spheres by numerical models based on the Method of Dimensionality Reduction and the Boundary Element Method. Thereby we assume quasi-stationarity, the validity of the half-space hypothesis, short impact times and Amontons-Coulomb friction with a constant coefficient for both static and kinetic friction. As under these assumptions both methods are equivalent, their results differ only within the margin of a numerical error. The solution of the impact problem written in proper dimensionless variables will only depend on the two parameters necessary to describe the elastic problem and a sufficient set of variables to describe the influence of viscoelastic material behaviour; in the case of a standard solid this corresponds to two additional variables. The full solution of the impact problem is finally determined by comprehensive parameter studies and partly approximated by simple analytic expressions.