Why Does Poisson's Ratio Differ for Different Materials?

[Prathamesh]

For any rod Poisson's ratio should be
same i.e. 0.5 (we get this ans if we find
(dr/r) / (dl/l) ) assuming that
volume of rod always remains constant...
But why it is not so ?
We have different ratios for different materials..

 

[drvrm]

For any rod Poisson's ratio should be
same i.e. 0.5 (we get this ans if we find
(dr/r) / (dl/l) ) assuming that
volume of rod always remains constant...
But why it is not so ?
We have different ratios for different materials..

the materials try to keep their volume constant but intermolecular forces are 'realistic' forces and many a time it falls short and the ratio goes to 0.3 or such values. the hooks law which is used also can be said to be working approximations.

 

[Chestermiller]

For their volume to be constant, all materials would have to be incompressible.

 

[Mapes]

For their volume to be constant, all materials would have to be incompressible.

Not quite; they would only need to have a shear modulus of zero. A liquid would satisfy this requirement, even if it is not perfectly incompressible. You can conclude this from the identity $$\nu=\frac{3K-2G}{2(3K+G)}$$ where $\nu$ is the Poisson's ratio, $K$ is the bulk modulus, and $G$ is the shear modulus. Note that the Poisson's ratio is undefined for a perfectly incompressible material (i.e., one for which $K=\infty$).

 

[Chestermiller]

Not quite; they would only need to have a shear modulus of zero. A liquid would satisfy this requirement, even if it is not perfectly incompressible. You can conclude this from the identity $$\nu=\frac{3K-2G}{2(3K+G)}$$ where $\nu$ is the Poisson's ratio, $K$ is the bulk modulus, and $G$ is the shear modulus. Note that the Poisson's ratio is undefined for a perfectly incompressible material (i.e., one for which $K=\infty$).

If the shear modulus is zero, then Young's modulus is zero, which means that, unless the Poisson ratio is equal to 1/2, the bulk modulus is zero. If the Young's modulus is not zero and the Poisson ratio is equal to 1/2, the bulk modulus is infinite, and the material is incompressible.