Understanding Poisson's Ratio and Restrained Cylinders

Click For Summary

Discussion Overview

The discussion revolves around the concept of Poisson's ratio, particularly in the context of a restrained steel cylinder subjected to internal pressure. Participants explore the implications of constraints on the material's behavior and the definition of Poisson's ratio under these conditions.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions how Poisson's ratio applies when the longitudinal strain is zero due to vertical restraint, suggesting that dividing lateral strain by zero is problematic.
  • Another participant asserts that Poisson's ratio is a material property that remains unchanged regardless of constraints, indicating that the loading conditions do not affect the intrinsic properties of the material.
  • A follow-up inquiry seeks clarification on whether the ratio of strains in the described loading situation can still be considered Poisson's ratio.
  • There is mention of exotic materials that may exhibit varying properties, including negative Poisson's ratios, suggesting that the discussion could become complex depending on material behavior.
  • It is noted that for typical materials within the elastic range, loading conditions do not alter material properties.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of Poisson's ratio under constrained conditions, with some asserting it remains constant and others questioning its relevance in such scenarios. The discussion does not reach a consensus.

Contextual Notes

Participants acknowledge that the behavior of exotic materials may differ from conventional materials, introducing additional complexity to the discussion. The implications of combined loading conditions on the calculations are also noted.

Who May Find This Useful

This discussion may be of interest to those studying material science, mechanical engineering, or anyone exploring the properties of materials under various loading conditions.

Gaunt
Messages
2
Reaction score
0
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?
 
Physics news on Phys.org
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.
 
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?
 
Gaunt said:
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.
 

Similar threads

High School Why Does Poisson's Ratio Show Equal Transverse Strain in 3D Rectangles?
  • · Replies 1 ·
Replies
1
Views
1K
Graduate Calculate Young's modulus and Poisson's ratio
  • · Replies 2 ·
Replies
2
Views
2K
Engineering What is Poisson's ratio and how does it relate to stress and strain?
  • · Replies 1 ·
Replies
1
Views
2K
Understanding Poisson's Ratio and Its Effects
  • · Replies 7 ·
Replies
7
Views
3K
What Factors Affect the Calculation of Poisson's Ratio from Rosette Gauge Data?
  • · Replies 2 ·
Replies
2
Views
2K
Axial Deformation and Poisson's Ratio Calculation
  • · Replies 2 ·
Replies
2
Views
5K
Graduate Model pressure loss vs time for air in a cylinder w/ hole
  • · Replies 15 ·
Replies
15
Views
4K
Help to find force given a diameter reduction (Poissons Ratio)
  • · Replies 6 ·
Replies
6
Views
14K
Analysing 2 Material Cylinder w/ Internal Pressure 100 Units
  • · Replies 4 ·
Replies
4
Views
2K
Prove Poisson's Ratio is .5 for Small Strains
  • · Replies 2 ·
Replies
2
Views
8K