Bulk modulus

Definition

Bulk modulus (K) is the ratio of hydrostatic stress (p) on an object to the resulting volumetric strain (ε _v ), which is the ratio of volume change (ΔV) to the initial volume (V _o ).

Hydrostatic stress cannot produce shear stress ; however, principal stress acting in one direction produces strain in all three directions, as described by Hooke’s law and Poisson’s ratio (ν). Therefore,

$$ {\varepsilon}_v = {\varepsilon}_x+{\varepsilon}_y+{\varepsilon}_z $$

(1)

$$ {\varepsilon}_x = \frac{\sigma_x}{E}-\nu \frac{\sigma_y}{E}-\nu \frac{\sigma_z}{E} $$

(2a)

$$ {\varepsilon}_y = -\nu \frac{\sigma_x}{E}+\frac{\sigma_y}{E}-\nu \frac{\sigma_z}{E} $$

(2b)

$$ {\varepsilon}_z = -\nu \frac{\sigma_x}{E}-\nu \frac{\sigma_y}{E}+\frac{\sigma_z}{E} $$

(2c)

where E is the Young’s modulus . Combining Eqs. 1 and 2a, b, c

$$ {\varepsilon}_v =...