In stretching a wire work is done against internal restoring forces. This work is stored in the wire as elastic potential energy or strain energy.

If a force F acts along the length L of the wire of cross-section A and stretches it by x then

So the work done for an additional small increase dx in length,

Hence the total work done in increasing the length by l,      

This work done is stored in the wire.

Energy stored in wire

Dividing both sides by volume of the wire we get energy stored in per unit volume of wire.

[As AL = volume of wire]

 

Total energy stored in wire (U)	Energy stored in per unit volume of wire (UV)