What is called elastic potential energy? Write its different formulas.

(N/A) Elastic potential energy is the energy stored in a body due to its deformation (change in shape or size) within its elastic limit. When a deforming force is applied to an elastic body,work is done against the internal restoring forces. This work is stored in the body as elastic potential energy.
Let a wire of length $L$,area of cross-section $A$,and Young's modulus $Y$ be stretched by a force $F$ such that its extension is $\Delta L$.
The different formulas for elastic potential energy $(U)$ are:
$1$. In terms of force and extension: $U = \frac{1}{2} F \Delta L$
$2$. In terms of stress and strain: $U = \frac{1}{2} \times \text{stress} \times \text{strain} \times \text{volume}$
$3$. In terms of Young's modulus: $U = \frac{1}{2} Y \times (\text{strain})^2 \times \text{volume}$
$4$. Energy density (Energy per unit volume): $u = \frac{U}{V} = \frac{1}{2} \times \text{stress} \times \text{strain} = \frac{1}{2} \frac{(\text{stress})^2}{Y}$