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I want to know the shape of a rubber ball when it is sandwiched between two (not necessary parallel) plane.

If two plane is parallel, I think it is possible to approximate the ball as spheroid and determine the two parameters by using the constantness of its volume and distance of two plane. However, when the planes are not parallel, I don't know how the ball looks like.

I guess I need some parameters like elasticity, but I don't have much physical knowledge.

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  • $\begingroup$ Is the ball solid or hollow like a tennis ball? Hollow balls deform in more complex ways. $\endgroup$ – RedGrittyBrick Nov 3 '15 at 11:05
  • $\begingroup$ The ball is solid. $\endgroup$ – user97452 Nov 3 '15 at 11:10
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    $\begingroup$ A spheroid is likely a very poor approximation, especially when you take into account contact areas and the deformation due to frictional forces for non-parallel plates. $\endgroup$ – RedGrittyBrick Nov 3 '15 at 11:12
  • $\begingroup$ Related: What is the stiffness of a crushed rod?. $\endgroup$ – John Alexiou Mar 8 '18 at 13:46
  • $\begingroup$ The deformation shape of a sphere is rather complex in general: youtube.com/watch?v=aMqM13EUSKw $\endgroup$ – John Alexiou Mar 8 '18 at 14:20
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Deformation of a rubber ball between planes

See: Elastic Compression of Spheres, Sphere Between Two Parallel Planes, page 9.

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  • $\begingroup$ Although this is a great reference, it only considers small deflections (linear strain theory). In addition, being based on Hertzian theory it only considers the deformation of the elastic half plane and not the gross deformations of the part under strain. So this is an incomplete picture of the entire deflection of a sphere. What I mean is that the overall geometry of the part isn't considered, just the shape of the contacting surfaces near the contact. $\endgroup$ – John Alexiou Mar 8 '18 at 14:17

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