Analytic contact solutions of the Boussinesq and Cattaneo problems for an ellipsoidal power-law indenter

Abstract Based on Galin’s theorem for the indentation of an elastic half-space by a polynomial punch and Barber’s determination contact area in normal problems, exact solution is developed frictionless ellipsoidal power-law punch. Within Cattaneo–Mindlin-approximation tangential contacts, problem with friction can be reduced to via Ciavarella–Jäger principle, based which also indenter given. All known solutions special cases (axisymmetric contact, elliptical Hertzian contact) are exactly recovered. A comparison pressure distribution obtained analytically 4-th power corresponding numerical boundary element method shows no noticeable differences. The proposed procedure used arbitrary finite superposition profiles, and, approximate sense, applicable monotonous profiles.