## Compressibility Modulus

What material modulus property is used to characterize compressibility?

##
__
__**Hint**

**Hint**

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

where
$$E$$
is the modulus of elasticity (Young’s modulus), and
$$\upsilon$$
is Poisson’s ratio.

##
__
__**Hint 2**

**Hint 2**

Poisson’s ratio is:

$$$\upsilon=-\frac{\varepsilon_{lateral}}{\varepsilon_{longitudinal}}$$$

where
$$\varepsilon_{lateral}$$
is the lateral strain, and
$$\varepsilon_{longitudinal}$$
is the longitudinal strain.

The Bulk (Volume) Modulus of Elasticity is a material property that characterizes a substance’s resistance to compression when subjected to pressure. The SI unit for the bulk modulus of elasticity is
$$N/m^2$$
(Pa), while the imperial unit is
$$lb_f/in^2$$
(psi). It is the ratio between increased pressure and decreased volume of a material, and it can be expressed in terms of Young’s modulus and Poisson’s ratio:

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

where
$$K$$
is the bulk (volume) modulus of elasticity,
$$E$$
is the modulus of elasticity (Young’s modulus), and
$$\upsilon$$
is Poisson’s ratio.

Poisson’s ratio measures a material’s deformation in directions perpendicular to the loading/pressure direction:

$$$\upsilon=-\frac{\varepsilon_{lateral}}{\varepsilon_{longitudinal}}$$$

where
$$\varepsilon_{lateral}$$
is the lateral strain, and
$$\varepsilon_{longitudinal}$$
is the longitudinal strain.

Young’s modulus describes the relationship between stress and strain during elastic loading. Applying Hooke’s Law:

$$$E=\frac{\sigma}{\varepsilon}$$$

where
$$\sigma$$
is the stress and
$$\varepsilon$$
is the strain.

Bulk (Volume) Modulus of Elasticity