Elastic energy density of compression via strain

Volumetric density of the elastic energy of a body is proportional to its Young’s modulus and the square of its strain. The Hooke’s law can be used to obtain analogous forms of this law.

Conditions:

1. The material is linearly elastic.

Links:

1. Wikipedia, equation on the fourth line.

elastic_energy_density

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

Symbol:

w

Latex:

\(w\)

Dimension:

energy/volume

young_modulus

young_modulus of the body’s material.

Symbol:

E

Latex:

\(E\)

Dimension:

pressure

engineering_normal_strain

engineering_normal_strain of the deformed body.

Symbol:

e

Latex:

\(e\)

Dimension:

dimensionless

law

w = E * e^2 / 2

Latex:

\[w = \frac{E e^{2}}{2}\]