Energy Stored (Elastic Strain Energy)

We can calculate the energy stored in a stretched material by considering the work done on it.

We defined work done as the force x distance moved in the direction of the force or

Work done is equal to the energy transferred, in this case transferred to the material, so:

The distance moved is the extension of the material, e, making the equation:

The force is not constant; it increases from zero to a maximum of F. The average force is given by:

If we bring these terms together we get the equation which simplifies to:

This is also equal to the area under the graph of force against extension.

We can write a second version of this equation by substituting our top equation of into the one above.