Work done in stretching a wire

Consider electric wire is under the force F. This force stretches the wire through small elongation x

let length of wire, L

Force produce an extension, X

Work done on wire = Area  covered on the x axis = Average force x  extension

Work done = 1/2 FE = 1/2 9YAxx/ L)

Since,  Y = F/A/X/L, = FL/Ax = YAX/L

W = YAX2/2L

W/AL = 1/2 (Yx/L)(x/L)

Energy stored per unit volume in stretching wire is 0.5 x stress x strain