  The elastic and adhesive properties of a solid surface can be quantified by
indenting it with a rigid sphere. Indentation tests are classically described
by the JKR-law when the solid is very stiff, while recent work highlights the
importance of surface tension for exceedingly soft materials. Here we show that
surface tension plays a crucial role even for stiff solids: it regularizes the
crack-like singularity at the edge of the contact. We find that the edge region
exhibits a universal, self-similar structure that emerges from the balance of
surface tension and elasticity. The similarity theory provides a complete
description for adhesive contacts, reconciling the global adhesion laws and
local contact mechanics.
