Question

Derive an expression for strain energy per unit volume of the material of a wire.​

Answer 1

Explanation:

The expression for strain energy is 1/2 × stress × strain.

The energy stored in a body is the strain energy, and the per unit volume is strain energy density, when a work is done on it by an external force to stretch or deform the body.

Strain energy = U = 0.5 Fl,  where f is external force applied to produce an extension 'i.

The strain energy density, u = U/V = (0.5 F l)/V

or u = 1/2 F/A l/L where A is the area and L is the length of the body before the external force is applied V = AL)

or u = 1/2 × stress × strain

Thus the energy density of a strained wire or the potential energy per unit volume of a stretched wire is derived.