Consider a cubical volume element with ribs dx, dy and dz which is subjected to a normal stress in the z direction. The force caused by the normal stress is equal to the stress multiplied with the surface area: The work done by this force is equal to the stored strain energy in the material, assuming no dissipation. Work is defined as the average force multiplied with the displacement. The average force needed to deform the element: The displacement is not known, but it can be written as the multiplication of the strain and the height of the volume element: This lead leads to the formula for the work. The term dx dy dz equals the volume dV: Assuming no heat loss, the provided work is equal to the internal energy which is called strain energy U. Hooke's law determines a relation between the normal stress and strain, wich means the strain energy density can be written like this: In the above equation E is the modulus of elasticity of the material.