# Whats the contact area for elastic contact between a cylinder and a plane surface?

I am trying to determine the contact area between a cylinder and a plane surface of two different materials so that the plane lies tangent to the cylinder. There is elastic contact between the two materials so the plane surface deforms to create a contact area around an area of the cylinder because there is a force pushing down on the cylinder (its weight).

I have looked around the internet and have only been able to find the scenarios for a sphere on a plane surface, two spheres in contact, and a cylinder on a plane surface but the but the cylinder's flat top is touching the plane instead of the plane being tangent.

It would be great if anyone could guide me to this equation.

-
I think the solution on wikipedia for a sphere and a half-space would be a useful starting point. Think about the way a cylinder differs from a sphere and how this changes the calculation. An assumption you can probably safely make is that the elastic solid will not bend around the flat top part of the cylinder. So your problem is essentially 2D. en.wikipedia.org/wiki/… – Michiel Mar 8 '13 at 6:27
That's what I was thinking as well; I didn't know if there is an actual formula for it. Thank you – Greg Harrington Mar 8 '13 at 6:56