Bulk modulus

One of the elastic moduli, sometimes called incompressibility, volumetric modulus, or stiffness.

Definition

 * $$\mathrm{bulk}\ \mathrm{modulus} = \frac{\mathrm{volume}\ \mathrm{stress}}{\mathrm{volume}\ \mathrm{strain}}$$


 * $$K = \frac{P}{\Delta V / V}$$

In terms of VP and VP

 * $$K = \rho\left(V_\mathrm{P}^2 - \frac43 V_\mathrm{S}^2 \right)$$

Other expressions
K can also be expressed in terms of Young's modulus, E, and Poisson's ratio, &nu;. This could be thought of as 'the engineer's perspective':


 * $$K = \frac{E}{3(1-2\nu)}$$

The 'rock physics perspective' casts K in terms of the 1st Lamé parameter &lambda; and shear modulus &mu;:


 * $$K = \lambda + \frac23 \mu$$

Upper and lower bounds on the constituent mixture of two materials can be obtained using Voight, Reuss, Hill and Hashin-Shtrikman bounds.