Elastic energy density of bulk compression via pressure

Volumetric density of the elastic energy of a body that is under bulk compression is proportional to the square of the pressure in the body and inversely proportional to the bulk modulus of the body’s material.

Conditions:

  1. The body undergoes bulk compression.

Links:

  1. Formula 77.5 on p. 393 of “General Course of Physics” (Obschiy kurs fiziki), vol. 1 by Sivukhin D.V. (1979).

elastic_energy_density

Elastic energy of the deformed body per unit of its volume. See energy_density

Symbol:

w

Latex:

\(w\)

Dimension:

energy/volume

pressure

pressure in the deformed body.

Symbol:

p

Latex:

\(p\)

Dimension:

pressure

bulk_modulus

bulk_modulus of the material.

Symbol:

K

Latex:

\(K\)

Dimension:

pressure

law

w = p^2 / (2 * K)

Latex:
\[w = \frac{p^{2}}{2 K}\]