Pressures distribution: solid sphere on a flat surface

In summary: 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.
  • #1
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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?

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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?
 
  • #3
lightarrow said:
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.
 
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  • #4
256bits said:
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.

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

What is pressure distribution?

Pressure distribution refers to how the pressure is distributed over a surface. In the context of a solid sphere on a flat surface, it refers to how the weight of the sphere is distributed over the surface it is resting on.

How is pressure distribution affected by the shape of the solid sphere?

The shape of the solid sphere affects the pressure distribution because it determines how the weight of the sphere is distributed over the surface. A spherical shape will distribute the weight evenly, while a non-spherical shape will result in uneven pressure distribution.

What factors influence the pressure distribution of a solid sphere on a flat surface?

The factors that influence pressure distribution include the weight and shape of the solid sphere, the surface area of the sphere in contact with the flat surface, and the properties of the surface, such as its hardness and roughness.

How does the pressure distribution change as the weight of the solid sphere increases?

As the weight of the solid sphere increases, the pressure distribution will also increase. This is because the weight is being distributed over a larger surface area, resulting in a higher pressure being exerted on the surface.

What is the significance of understanding pressure distribution in engineering and design?

Understanding pressure distribution is important in engineering and design because it allows for the proper distribution of weight and forces on a surface, which can affect the stability and structural integrity of a structure. It also helps in determining the most efficient and effective design for a given application.

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