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
:doc:`Hooke's law <laws.dynamics.deformation.tensile_stress_is_youngs_modulus_times_strain>`
can be used to obtain analogous forms of this law.

**Conditions:**

#. The material is linearly elastic.

**Links:**

#. `Wikipedia, equation on the fourth line <https://en.wikipedia.org/wiki/Young%27s_modulus#Elastic_potential_energy>`__.

.. py:currentmodule:: symplyphysics.laws.dynamics.deformation.elastic_energy_density_of_compression_via_strain

.. py:data:: elastic_energy_density

    Elastic energy of the deformed body per unit of its volume. See :attr:`~symplyphysics.symbols.basic.energy_density`

Symbol:
    :code:`w`

Latex:
    :math:`w`

Dimension:
    :code:`energy/volume`


.. py:data:: young_modulus

    :attr:`~symplyphysics.symbols.classical_mechanics.young_modulus` of the body's material.

Symbol:
    :code:`E`

Latex:
    :math:`E`

Dimension:
    :code:`pressure`


.. py:data:: engineering_normal_strain

    :attr:`~symplyphysics.symbols.classical_mechanics.engineering_normal_strain` of the deformed body.

Symbol:
    :code:`e`

Latex:
    :math:`e`

Dimension:
    :code:`dimensionless`


.. py:data:: law

    :code:`w = E * e^2 / 2`


    Latex:
        .. math::
            w = \frac{E e^{2}}{2}