# Elastic Strain Energy

- Up to the elastic limit of a sample, all the work done in stretching it is stored potential energy, or
**Elastic Strain Energy**. This value can be determined by calculating the**area under the the force-extension graph**. If the sample obeys Hooke’s Law, and is below the elastic limit, the Elastic Strain Energy can be calculated by the formula:

**E = ½Fx**

- Or, since
**F = kx**(where k is the stiffness constant of the sample):

**E = ½kx**

^{2}

- Some force-extension graphs have two curves, one measured when force was being applied (
**loading**) and one where that force was being removed (**unloading**). The unloading curve may be below the loading curve, which would mean that**less energy is given out when a force is removed from the sample than was put in**, as the area under the unloading curve is less than that of the loading curve. This is because some of the energy put into the material was**transferred as waste energy**, like heat.