No slip boundary condition:

Let's say that the surface of the solid adheres completely onto the punch, so that there is no slippage of the solid, then we can have the following boundary condition:

and	(5.10)

Where and are the displacements of the punch.

We can then write following coupled equations for the displacements from equation 4.27, in which the slope of the displacements underneath the punch are zero:

	(5.11)

Adding the two equations, we can have

	(5.12)

Equation 5.12 is of the general form

,

Which has the solution,

	(5.13)

Where,     and

So the solution is obtained as,

	(5.14)