Pressures distribution: solid sphere on a flat surface

[lightarrow]

In a real case (not ideally rigid bodies), a (e. g.) hard metal sphere is on a flat (e. g.) hard metal surface (a table) and the sphere is "charged" vertically on the table by a vertical force directed downward. In this situation, an engineer told me that the maximum pressure on the table is not localized in the contact point but in a region, close, but under that point. Is it true? If it is, why?

--
lightarrow

 

[Chestermiller]

I don’t quite follow. Can you provide a diagram showing where he thinks the maximum pressure (compressive normal stress or isotopic portion of stress tensor) is located?

 

[256bits]

the maximum pressure on the table is not localized in the contact point but in a region, close, but under that point

If the contact point does NOT deform there would be an infinite stress at that point, which for real materials does not happen.
Instead some elastic deformation occurs, redistributing the stress within a small area, or volume.
Of course if the stresses become too great, plastic deformation will occur and the material(s) will generally begin to fail under those conditions.

Please read this for more information
http://mech.utah.edu/~me7960/lectures/Topic7-ContactStressesAndDeformations.pdf
@Chestermiller can probably guide you through that quite thoroughly, if that is what you are inquiring about.

 

[lightarrow]

If the contact point does NOT deform there would be an infinite stress at that point, which for real materials does not happen.
Instead some elastic deformation occurs, redistributing the stress within a small area, or volume.
Of course if the stresses become too great, plastic deformation will occur and the material(s) will generally begin to fail under those conditions.

Please read this for more information
http://mech.utah.edu/~me7960/lectures/Topic7-ContactStressesAndDeformations.pdf
@Chestermiller can probably guide you through that quite thoroughly, if that is what you are inquiring about.

Thanks. Slide 7-8 addresses exactly my question: "The maximum shear and Von Mises stress are reached below the contact area•This causes pitting where little pieces of material break out ofthe surface".

Infact the engineer I talked with began explaining me why in some situations (we were talking of small wheels with a great weight on them) the pavement is damaged under the contact point and that with bearings this can cause pitting (this would have been my next related question).

To Chestermiller: sorry I couldn't provide a picture, I'm out with a smartphone only. My friend engineer talked of a sort of "onion like" region under the contact area.
Thank you for your answeres.

--
lightarrow

 

[Chestermiller]

In my judgment, at least qualitatively, @256bits response answers your question.