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.