Bulk modulus via Young modulus and Poisson ratio

Suppose a uniform isotropic body is subjected to bulk compression, i.e. forces are applied to it from all its sides. Then the bulk modulus is the proportionality coefficient between relative volume change of the body and the pressure inside of it. It is proportional to the Young modulus of the material and also depends on its Poisson ratio.

Conditions:

1. The body is isotropic and uniform.

2. The Poisson ratio \(\nu < \frac{1}{2}\), since elastic energy density cannot be negative.

Links:

1. Wikipedia, derivable from second part of the equation.

bulk_modulus

bulk_modulus of the material.

Symbol:

K

Latex:

\(K\)

Dimension:

pressure

young_modulus

young_modulus of the material.

Symbol:

E

Latex:

\(E\)

Dimension:

pressure

poisson_ratio

poisson_ratio of the material.

Symbol:

nu

Latex:

\(\nu\)

Dimension:

dimensionless

law

K = E / (3 * (1 - 2 * nu))

Latex:

\[K = \frac{E}{3 \left(1 - 2 \nu\right)}\]