This model has a simple closed-form analytical expression, matching with finite element results nearly perfectly.

Ref: G. Feng, S. Qu, Y. Huang and W.D. Nix, An analytical expression for the stress field around an elastoplastic indentation/contact, Acta Materialia, V.55, 2007, P2929-2938. http://dx.doi.org/10.1016/j.actamat.2006.12.030