The oblique impact of a rigid sphere on a power-law graded elastic half-space

The low-velocity oblique impact of a rigid sphere on a power-law graded elastic half-space is studied under the assumptions of elastic similarity and a constant coefficient of friction. The normal component of motion is determined analytically. The tangential problem is investigated numerically using the Method of Dimensionality Reduction. We find that the solution of the impact problem written in proper dimensionless variables is the same as in the homogeneous case. This solution therefore can possibly be generalised for arbitrary inhomogeneous material behaviour, if the Mindlin ratio has no spatial dependence. However, different physical ranges are possible for the dimensionless variables in the homogenenous and inhomogeneous cases, which is why, in the case of power-law grading, parameter combinations are possible, for which no kinetic energy is dissipated during the impact. The maximum contact pressures during normal impact can be significantly reduced by the usage of power-law grading.