Motivated by the structure of the normal surface stress of the extended Hertzian approach  given due to terms of the form r^2n*(a^2-r^2)^(1/2) (n=0, 2, 4, 6…) it seems attractive to evaluate the complete elastic field also for shear loadings of this form. The reason for this lays in the demand for analytical tools for the description of mixed loading conditions as they appear for example in scratch experiments.
 N. Schwarzer, "Elastic Surface Deformation due to Indenters with Arbitrary symmetry of revolution", J. Phys. D: Appl. Phys., 37 (2004) 2761-2772