Introduction to Elasticity/Hertz contact
The Hertz Problem: Rigid Cylindrical Punch 
- The contact length depends on the load .
- There is no singularity at .
- The radius of the cylinder () is large.
Plug back into the expression for to get
This expression is singular at and , unless we choose
Plugging into the equation for ,
Two deformable cylinders 
If instead of the half-plane we have an cylinder; and instead of the rigid cylinder we have a deformable cylinder, then a similar approach can be used to obtain the contact length
and the force distribution