When a material is subjected to an axial loading, it experiences normal stress, leading to strain energy generation. This equation is valid for uniformly distributed stress, and the strain energy density is constant throughout the material.

For a material having non-uniform stress distribution, the strain energy density is defined for the small volume of the material.

Here, strain energy density is expressed as the product of the applied stress and the produced strain.

Integrating strain energy density over the entire volume of the material gives the total strain energy stored in the material.

The obtained equation for strain energy only applies to elastic deformation and is also termed elastic strain energy.

When the material is subjected to centric axial loading, the normal stresses are assumed to be uniform over any transverse section. Here, the normal stress is written as the ratio of the internal forces to the cross-sectional area under consideration.

The strain energy stored in such cases is written in terms of internal force and the modulus of elasticity.