Stresses and strain : change of volume I was reading about stresses and strains and I came across the concept of volumetric strain and am now having a slight conceptual difficulty. I used to believe that despite changes in linear and lateral dimensions due to stresses, volume remains constant. Could someone please clarify if the body's volume really does increasing and how does this physically occur ?
 A: You can break down the elastic properties to two effects. $G$ the shear modulus and $K$ the bulk modulus. There is a great conversion table at wikipedia about it.
Given the elastic modulus $E$ and Poisson's ratio $\nu$ the above properties are
$$ \begin{align} G & = \frac{E}{2(1+\nu)} & K & = \frac{E}{3(1-2\nu)} \end{align} $$
Now the shear modulus $G$ is the resistance to shear deformation (which preserves volume) and bulk modulus $K$ is the resistance to volume changes due to hydrfostatic pressures (all stress components are equal). To find a material with no volumetric changes under any loading, you have to find $K=\infty$ or $\nu=0.5$.  Any material with $\nu<0.5$ will have a positive bult modulus meaning its volume will actually reduce on comrpessive stresses.
The definion of bulk modulus is
$$ K = -V \frac{{\rm d} P}{{\rm d} V} $$ where $P$ is the hydrostatic pressure and $V>0$ the volume. 
A positive $K$ means ${\rm d}V = -\frac{V}{K} {\rm d}P$ or the volume descreases with pressure (like being underwater).
