The Hertz problem : rigid cylindrical punch edit

Hertz indentation
  • The contact length   depends on the load  .
  • There is no singularity at  .
  • The radius of the cylinder ( ) is large.

We have,










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 edit

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