Introduction to Elasticity/Hertz contact

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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,

Hence,

and

Therefore,

and

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