Hertz Contact Solution of Elastic Theory for Concave to Convex Shapes

In summary, the equation calculates contact stress between two objects with different elastic moduli and Poisson's ratios. The second part of the equation approaches 0 as the two radii get closer, resulting in a contact stress of 0 when the two radii are equal. This may seem confusing, but it can be explained by the fact that the contact area becomes the entire surface area of each object, resulting in a very small contact stress due to the load being spread over a larger area. This was confirmed by the conversation participants.
  • #1
vdash103
8
0
For the equation:

contact stress = {(1 / (pi[((1-v1^2)/E1)) + ((1-v2^2)/E2))) ^ 0.5} * {((Fn/b) * (Sum (1/pi)))^0.5}

Where Sum (1/pi) = [(1/p1) - (1/p2)] for concave shapes in contact with convex shapes

Sum (1/pi) approaches 0 as the two radii get closer, however when the two radii equal each other, the second part of the equation equals 0 from multiplication and the entire equation will equal 0. This is confusing to me. How could the stress be 0?
 
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  • #2
If the two radii are equal, wouldn't the contact area by the entire surface area of each object? Then the contact stress would be very small, as the constant load would be spread over a very large area.
 
  • #3
I believe that is correct. That was the assumption I had come to.
 

1. What is the Hertz Contact Solution of Elastic Theory for Concave to Convex Shapes?

The Hertz Contact Solution of Elastic Theory is a mathematical model that describes the contact between two elastic bodies with concave and convex shapes. It is used to calculate the distribution of stress and deformation at the contact interface between the two bodies.

2. How is the Hertz Contact Solution of Elastic Theory applied?

The Hertz Contact Solution of Elastic Theory is applied by using a set of equations that take into account the geometry, material properties, and applied load of the two bodies. It provides a solution for the contact pressure, contact area, and deformation at the contact interface.

3. What are the assumptions made in the Hertz Contact Solution of Elastic Theory?

The Hertz Contact Solution of Elastic Theory makes several assumptions, including that the bodies are perfectly elastic, smooth, and have a small contact area compared to their overall surface area. It also assumes that the bodies are in pure rolling motion and there is no adhesive or frictional forces present.

4. What is the difference between concave and convex shapes in the Hertz Contact Solution of Elastic Theory?

In the Hertz Contact Solution of Elastic Theory, the concave shape refers to a body that has a curved surface that is facing inward, while the convex shape refers to a body that has a curved surface facing outward. The difference between the two shapes affects the amount of contact pressure and deformation at the contact interface.

5. What are the limitations of the Hertz Contact Solution of Elastic Theory?

The Hertz Contact Solution of Elastic Theory has some limitations, including that it only applies to elastic bodies and does not take into account plastic deformation or failure. It also assumes that the bodies have a uniform material property and that the contact area remains constant throughout the loading process.

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