Work done = energy stored

\(W=\frac{1}{2} \times \text { force } \times \text { elongation }\) \(\left\{\right.\) Force \(=\frac{\Delta L}{L} \cdot A Y\)

\(W=\frac{1}{2} \times \frac{\Delta L}{L} \times A \times Y \times \Delta L\)

\(W=\frac{1}{2} \frac{A Y}{L} \times \Delta L^2\)

\(W \propto \Delta L^2\)