Elastic Strain Energy

We can build on the idea of energy stored from the previous lesson now that we know what stress and strain are. We can work out the amount of elastic strain energy that is stored per unit volume of the material.

It is given by the equation:

There are two routes we can take to arrive at this result:

Equations

If we start with the equation for the total energy stored in the material:

The volume of the material is given by:

Now divide the total energy stored by the volume: which can be written as:

If we compare the equation to the equations we know for stress and strain we see that:

Graphs

The area under a stress-strain graph gives us the elastic strain energy per unit volume (m³). The area is given by:

or