Rigid flat punch

Consider now the problem of a frictionless rigid punch which presses an elastic half space. Since the punch is rigid, the surface of the elastic solid must remain flat where it is in contact with the punch. In addition to that we assume the condition that the punch does not tilt, so that the interface remains parallel to the undeformed surface of the solid. So our first boundary condition is

constant	(5.1)

We can consider following situations:

(a) Surface of the punch is frictionless, so that		(5.2a)
(b) Friction at the interface is sufficient to prevent any slip      between the punch and the surface of the solid:		(5.2b)
(c) Partial sip occurs to limit the tangential traction		(5.2c)