 Solution

An isotropic linear elastic solid has two independent elastic constants. For infinitesimal strain,The shear modulus $G$ governs shape change and the bulk modulus $K$ governs volume change. Young's modulus $E$ and Poisson's ratio $\nu$ are equivalent parameters:Positive strain energy requires $G,K>0$, hence $-1<\nu <1/2$; $\nu \to 1/2$ is the incompressible limit. Small-amplitude bulk waves have speeds $c_P=\sqrt{(K+4G/3)/\rho }$ and $c_S=\sqrt{G/\rho }$. Isotropy removes directional dependence, not the distinction between compression and shear. These laws apply within the elastic small-strain regime, not after yielding or fracture.