Calculating Poisson's Ratio with a Modulus of Rigidity & Young's Modulus

In summary, the conversation discusses how to calculate the expected value of Poisson's Ratio for a material with a given modulus of rigidity and Young's Modulus. The formula for calculating Poisson's Ratio is mentioned and a helpful resource is provided for further understanding.
  • #1
mattjones
5
0
Hi, I'm wondering if someone can point me in the right direction with this question.

A material has a modulus of rigidity of 100 GNm-2 and a Young's Modulus of 250 GNm-2. Calculate the expected value of Poisson's Ratio for the material.

Poisson's Ratio is expressed as transverse strain / axial strain

So how am I supposed to work this out when the only information I am given is what's above? Or am I misunderstanding the question?

Any help would be appreciated

Thanks

Matt
 
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  • #2
mattjones said:
Hi, I'm wondering if someone can point me in the right direction with this question.

A material has a modulus of rigidity of 100 GNm-2 and a Young's Modulus of 250 GNm-2. Calculate the expected value of Poisson's Ratio for the material.

Poisson's Ratio is expressed as transverse strain / axial strain

So how am I supposed to work this out when the only information I am given is what's above? Or am I misunderstanding the question?

Any help would be appreciated

Thanks

Matt

For isotropic materials, there is a formula which relates E, G, and poisson's ratio. It's in just about every strength of materials text ever published.

For a quick refresher, look at this attachment:

http://www.colorado.edu/engineering/CAS/courses.d/Structures.d/IAST.Lect05.d/IAST.Lect05.pdf

Check out pp. 7 & 8.
 
  • #3
Thanks very much for that, I'll get reading!
 

1. What is Poisson's Ratio?

Poisson's Ratio is a measure of the ratio of lateral strain to the corresponding axial strain when a material is subjected to tensile stress. It is a dimensionless quantity and is denoted by the Greek letter "nu" (ν).

2. How is Poisson's Ratio calculated?

Poisson's Ratio can be calculated using the formula ν = -lateral strain/axial strain. The lateral strain can be determined by measuring the change in width of the material and the axial strain can be determined by measuring the change in length of the material.

3. What is the Modulus of Rigidity?

The Modulus of Rigidity, also known as shear modulus, is a measure of a material's ability to withstand shear stress. It is defined as the ratio of shear stress to shear strain within the elastic limit of the material.

4. How is the Modulus of Rigidity related to Poisson's Ratio and Young's Modulus?

There is a relationship between Poisson's Ratio, Modulus of Rigidity, and Young's Modulus. The Modulus of Rigidity can be calculated using the formula G = E/2(1+ν), where E is the Young's Modulus and ν is Poisson's Ratio. This means that the Modulus of Rigidity is dependent on both Poisson's Ratio and Young's Modulus.

5. Can Poisson's Ratio be negative?

Yes, Poisson's Ratio can be negative for certain materials under specific conditions. This means that the material experiences a decrease in lateral strain while under tension, instead of the expected increase. Negative Poisson's Ratio materials are also known as auxetic materials and have unique properties that make them useful in various applications.

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