# Young's Modulus and volume

After a tough discussion with my friends, I opt to ask here because we aren't coming to an answer.
When stress is applied to a solid, lets say an iron rod, will the volume change, or when the length of the rod shrinks or stretches, the area of the cross sectional area will reduce or increase to maintain a constant volume?

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Conservation of mass... the volume is the same and poisson's ratio helps tell how much the cross sectional area will change.

That was exactly what I was looking for, thanks!

Dilatation or volume change can be given for small strains in an isotropic linear elastic material by:

$$\frac{dV}{V}=\frac{1-2\nu}{E}(\sigma_{x}+\sigma_{y}+\sigma_{z})$$

In a uniaxial tensile test at small strains, $\sigma_{y}=\sigma{z}=0$. You can see that for there to be no volume change, $\nu$ (Poisson's ratio) must be equal to 0.5 at which point the material is said to be incompressible, as the bulk modulus tends to infinity.

Typically, most metals exhibit Poisson's ratios of between 0.3 and 0.35, meaning you will observe some volume change at low strains. Rubbers have Poisson's ratios tending to 0.5, meaning you will exhibit little to no volume change.