Upper and lower bounds to indentation of rigid ball into semi-infinite solid

Comparisons between the suggested bounding analysis and experiments (taken from Tabor [Tabor D. Hardness of Metals. Oxford: Clarendon Press; 1951], Johnson [Johnson KL. Contact mechanics. Cambridge: Cambridge University Press; 1985 (new edition, 2001)] and others), numerical FEM solutions (Mesarovic and Fleck [Mesarovic SDj, Fleck N. Spherical indentation of elastic-plastic solids. Proceedings of Royal Society of London 1999; A455: 2707-28] and others) and some self-made measurements are all favorable.