# Poisson's ratio

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..

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.

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

Prathamesh
Mapes
Homework Helper
Gold Member
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
Mentor
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.