Elastic energy is a form of potential energy that is stored in the bonds between atoms in an object or substance when it is temporarily under stress. This stress could be due to the object being stretched, compressed, or twisted. When a force acts on an object, it can cause it to temporarily change its shape, and the object stores elastic energy as a result. Elastic energy occurs when objects are impermanently compressed, stretched, or generally deformed in any manner. Elasticity theory primarily develops formalisms for the mechanics of solid bodies and materials.

Some examples of objects that can store elastic energy include elastic bands, squishy balls, a bow and arrow, coiled springs, catapults, and slingshots. An object designed to store elastic potential energy will typically have a high elastic limit, but all elastic objects have a limit to the load they can sustain. When deformed beyond the elastic limit, the object will no longer return to its original shape.

The elastic potential energy equation is used in calculations of positions of mechanical equilibrium. The elastic potential energy per unit volume is given by the equation:

$$\frac{1}{2} \frac{F^2}{A_0 Y}$$

where F is the force applied, A0 is the cross-sectional area, and Y is the Youngs modulus of the material.

In summary, elastic energy is a type of potential energy that is stored in an object or substance when it is temporarily under stress due to being stretched, compressed, or twisted. It is an important concept in the mechanics of solid bodies and materials.