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Work done in stretching a wire

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
48365.png  48358.png
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, 48338.png
Dividing both sides by volume of the wire, we get energy stored in per unit volume of wire.
[as AL = volume of wire]

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