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

In summary, the conversation discusses the need to calculate Young's modulus based on the deformation of a sphere into an ellipsoid, assuming a deforming force acting along one axis. The initial dimensions of the object before and after deformation are known. The conversation also mentions the use of references and the difficulty in determining the stress distribution at the surface of the sphere.
  • #1
Dilema
37
1
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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  • #2
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 ?
 
  • #3
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).
 
  • #4
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
 
  • #5
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?
 
  • #6
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
 
  • #7
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.
 

What is Young's modulus?

Young's modulus, also known as the elastic modulus, is a measure of the stiffness of a material. It describes the ratio of stress (force per unit area) to strain (deformation) in a material when subjected to an applied force.

How is Young's modulus calculated?

Young's modulus is typically calculated by dividing the stress (force per unit area) by the strain (change in length/original length) of a material. The resulting unit is typically in Pascals (Pa) or Newtons per square meter (N/m^2).

What factors affect Young's modulus?

The Young's modulus of a material is affected by several factors, including the type of material, its composition, temperature, and the rate of loading or deformation. Generally, stiffer materials have a higher Young's modulus.

Why is Young's modulus important?

Young's modulus is an important parameter in material science and engineering as it helps to characterize the mechanical properties of a material. It is used in the design and analysis of structures and components to ensure they can withstand the expected forces and stresses without breaking or deforming.

Can Young's modulus change over time?

Yes, Young's modulus can change over time as a result of external factors such as temperature, humidity, and exposure to chemicals or radiation. It can also change due to internal factors such as microstructural changes or defects within the material. These changes can affect the performance and durability of a material in different applications.

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