Strain energy is a fundamental concept in the field of materials science and structural engineering, describing the energy absorbed by a material or structure when it is deformed under load.

Consider a rod that is fixed at one end and subjected to an axial force at the free end. This axial force induces stress within the rod, leading to its elongation. As the axial force increases, so does the elongation of the rod, illustrating a direct relationship between the force applied and the resulting deformation. This behavior can be graphically represented by a load-deformation plot.

The work done by the axial force to elongate the rod by a small amount is equal to the product of the force and the corresponding elongation. Graphically, this work corresponds to the area under the load-deformation curve for a given elongation. To calculate the total work done on the rod for any given elongation, one must integrate the force-elongation equation over the elongation limits. This total work represents the energy input to the system, which is stored as strain energy. Within the elastic limit of the material, the strain energy U stored in the material due to elastic deformation is proportional to the square of the elongation.

The concept of strain energy allows engineers to quantify the energy absorption capacity of a material or component, which is essential for assessing its ability to withstand loads without undergoing permanent deformation or failure. Strain energy also plays a pivotal role in various engineering applications, such as the design of shock absorbers, energy storage devices, and in the analysis of impact forces.