A wire of length L and area of cross-section A is made of a material of Young’s modulus Y. If the wire is stretched by the amount x, the work done is

Y=FA×Lx When a wire is stretched, work is done against the inter atomic forces. This work is stored in wire in the form of elastic potential energy. So, W=12 stress × strain × volume = 12 (Y.strain)  × strain × volume=12Y×xL2×A×L=12YAx2L=YAx22L