How to Calculate Young's Modulus for Deformation of a Sphere into an Ellipsoid?

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Discussion Overview

The discussion revolves around calculating Young's modulus based on the deformation of a sphere into an ellipsoid under the influence of a deforming force. Participants explore the theoretical and practical aspects of this problem, including force distribution and stress analysis, while seeking references and clarifications on the topic.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant seeks guidance on calculating Young's modulus, assuming a deforming force acts along one axis and that initial and final dimensions are known.
  • Another participant questions the research efforts made by the original poster and asks for clarification on the nature of the problem.
  • A participant raises concerns about how the load is distributed over the sphere's surface, suggesting that point forces may not lead to the desired deformation.
  • Chestermiller states that the force is uniformly distributed over an area of the hemisphere, while Daven mentions looking for examples in specific theses and publications.
  • One participant expresses confusion about the problem's context, asking whether it involves an elastic sphere in a different medium or a spherical region within a larger medium.
  • Another participant acknowledges that the references provided are confusing and misleading, indicating a need for clearer problem description.
  • A later reply emphasizes the necessity of specifying the stress distribution at the sphere's surface to define the problem adequately.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the specifics of the problem or the necessary conditions for solving it. Multiple competing views regarding the force distribution and the context of the deformation remain unresolved.

Contextual Notes

Participants highlight limitations in the problem's specification, particularly regarding the stress distribution and traction at the sphere's surface, which are essential for a unique solution.

Dilema
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I need to calculate Young's modulus based on deformation of sphere into ellipsoid. I assume the deforming force acting along one axes. Initial dimensions of the object before (sphere) and after (ellipsoid) deformation are known.Does anyone know or familiar with good reference?
 
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Dilema said:
I need to calculate Young's modulus based on deformation of sphere into ellipsoid. I assume the deforming force acting along one axes. Initial dimensions of the object before (sphere) and after (ellipsoid) deformation are known.Does anyone know or familiar with good reference?
You have labelled you post with an A tag inferring you are post graduate level
What researching have you done so far to find an answer ?
 
Dilema said:
I need to calculate Young's modulus based on deformation of sphere into ellipsoid. I assume the deforming force acting along one axes. Initial dimensions of the object before (sphere) and after (ellipsoid) deformation are known.Does anyone know or familiar with good reference?
How is the load distributed over the surface of the sphere? (Point forces certainly won't result in a sphere deforming into an ellipsoid).
 
Chestermiller:
The force is uniformly distributed over an area of the hemisphere

Daven: I work in parallel

I was looking for example in a thesis entitled STRESS ANALYSIS OF AN ELLIPSOIDAL INCLUSION see link https://www.physicsforums.com/threads/calculating-youngs-modulus.944549/

I also tried to consider: http://www.sergiorica.com/Site/Publications_files/1998bPhilMag78.pdf
 
I still don't understand what you are asking. Is it related to having an elastic spheric ball immersed in another medium with a different elastic modulus, and you are subjecting the outer medium to a tensile load? Or is it that you have an identified spherical region within a larger medium, and you want to determine the modulus of the material based on the distortion of the spherical region into an ellipsoid as a result of applying a tensile load to the overall medium?
 
The references I put are confusing and misleading. I showed that I tried to get some inspiration as for how to solve my problem.

Please follow the link for a better description of the problem. I hope it is clearer.

https://drive.google.com/file/d/1kJtpLYN7Z30rR3LEK5-oTgC5mskzbkDb/view?usp=sharing
 
There is still insufficient information to solve this problem. It's easy to draw arrows for force distribution as you have done on the figure, but your really need to specify the stress distribution (at least the traction distribution) at the surface of the sphere to complete the specification of this problem. Saying that there are forces on the two sides is not sufficient to define a unique solution.
 

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