Strain energy
Any stress which is applied to a material will cause elastic deformation. The stored energy in a material caused by this strain is called the strain energy. The stored energy per unit volume is called the strain energy density.

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: Force caused by normal stress 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. Work of a force The average force needed to deform the element: Strain force The displacement is not known, but it can be written as the multiplication of the strain and the height of the volume element: Strain displacement This lead leads to the formula for the work. The term dx dy dz equals the volume dV: Work by strain 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: Strain energy In the above equation E is the modulus of elasticity of the material.

Strain energy density
When the strain energy formula is divided by the volume term, the strain energy density u is obtained: Strain energy density
Modulus of resilience
The maximum strain energy density which can be stored in a material until plastic deformation occurs, is called the modulus of resilience.