Bounded asymptotic solutions for incomplete contacts in partial slip

Abstract

Asymptotic solutions for the contact pressure and shearing tractions present adjacent to the edge of an incomplete contact are derived, and for each a dimensional scaling factor (akin to a generalised stress intensity factor), is defined. These two quantities may therefore be used to define the complete local stress state, for which purpose the Muskhelishvili potentials are derived. The application of this technique to a comparison of the Hertz–Cattaneo contact, the flat and rounded contact and the tiled punch is described, and the extent of the domain of validity of the asymptote found.