A wire of length $L$, area $A$ and Young's modulus $Y$ is stretched by hanging a mass $m$ from its free end. The elastic potential energy stored in the wire is

Stress $\sigma = mg/A$, strain $\varepsilon = \sigma/Y = mg/(AY)$, energy density $u = \tfrac{1}{2}\sigma\varepsilon = \dfrac{m^2g^2}{2A^2Y}$. Total energy $U = u\cdot V = u\cdot AL = \dfrac{m^2 g^2 L}{2 A Y}$.