Understanding Poisson's Ratio and Restrained Cylinders

[Gaunt]

Hey. I have a couple of questions about Poisson's ratio I hope you guys can answer.

If I have a cylinder made of, let's say steel. Steel has a Poisson's ratio of roughly 0.33. The cylinder is restrained in the vertical direction so no displacement can occur.

If I apply an internal pressure to the cylinder, it is going to expand laterally, but it can't in the vertical direction because it is restrained.

Seeing as the Poisson ratio is a ratio of lateral to longitudinal strains and the strain in the longitudinal direction will be zero, where does that leave the poisson ratio? If The longitudinal strain is zero, you cannot divide the lateral strain by zero!

Am I missing something?

 

[xxChrisxx]

Poissons ratio is a material property. Constraining the movement of a material does nothing to affect that,

In effect by constraining the ends, you are applying a load in tension to counter act the way the material would want to move if it were unconstrained. As you have two loads instead of one on the material very basic calculations will break down as you have combined loads.

 

[Gaunt]

Thanks for the quick reply.

So what you are saying is that regardless of loading conditions a material will always have the same poisson ratio?

Also, the ratio of strains in a loading situation as above wouldn't be Poisson's ratio then, would it?

 

[xxChrisxx]

Thanks for the quick reply.

So what you are saying is that regardless of loading conditions a material will always have the same poisson ratio?

Also, the ratio of strains in a loading situation as above wouldn't be Poisson's ratio then, would it?

This could open a can of worms depending on how detailed we get. As exotic materials can change properties, or even have negative poissons ratios.

In general for 'normal' materials loaded in the elastic range then yes. Loading conditions will not change material properties.

 

[pmacias]

Hello there, thank you for your questions about Poisson's ratio and restrained cylinders. Let me try to clarify some of your points.

Firstly, you are correct in understanding that Poisson's ratio is a ratio of lateral to longitudinal strains. In the case of your restrained cylinder, the longitudinal strain is indeed zero because it is constrained in that direction. However, this does not mean that the Poisson's ratio is undefined. Rather, it means that the lateral strain will be equal to zero as well, since the cylinder cannot expand laterally due to the constraint. Therefore, the Poisson's ratio in this case would still be 0.33, as it is a material property of steel and does not change based on the boundary conditions.

To further explain, Poisson's ratio is a measure of a material's resistance to lateral deformation when subjected to a longitudinal strain. In your example, the cylinder is experiencing a longitudinal strain due to the internal pressure, but since it is restrained in that direction, it cannot deform laterally. This does not change the fact that the material still has a Poisson's ratio of 0.33, which is a measure of its overall tendency to deform laterally when subjected to a longitudinal strain.

I hope this helps to clarify your understanding of Poisson's ratio and its application in the case of restrained cylinders. Please let me know if you have any further questions. Thank you.