Question

What is meant by the elastic potential energy? Calculate the elastic potential energy due to the longitudinal and volumetric strains. 

Answer 1

Elastic potential energy is potential energy stored as a result of deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring, which depends upon the spring constant k as well as the distance stretched. According to Hooke's law, the force required to stretch the spring will be directly proportional to the amount of stretch.

The elastic energy per unit volume is terms of longitudinal strain σ and Young's modulus Y is

$$E=\frac{1}{2}Y\sigma$$