Energy in deformations

Energy in deformations

Whenever we apply force to an object, it will cause deformation. If the deformation caused is within the elastic limit, the work done in deforming the object is stored within it as potential energy. We call this (elastic) 'strain energy'. It can be released from the object by removing the applied force. The strain energy then performs work in un-deforming the object and returns to its original state. We can calculate the energy stored in a deformed object, from the force- extension graph. As a example let us consider the case of a metal wire. The diagram is a force-extension graph of the wire within its elastic limit. It is a straight-line graph. If we apply a tensile force (T) of 10N to this wire it will extend to 0.02M.

The work (W) done by the wire is the shaded triangular area under the straight line.

In this example W is:.

W = ½ force x extension = ½ x 10 x 0.02 = 0.1J

The metal wire in the above example, stores energy perfectly as it releases all the energy stored in the form of extensional strain without any loss of energy.

Some materials cannot store energy perfectly. For example, rubber is not a good material for storing energy even though popularly it is called 'elastic'.

Actually, it does not obey Hooke's law. We can see this from its force-extension graph. We get two different curves, one for applying increasing force (loading curve) and a different one when we decrease the force (unloading curve). On unloading, rubber gives up less energy (area under the unloading line) than the energy it takes up to deform (area under the loading line). The difference between these two energies (area enclosed by the loop) is the energy lost. This energy loss is absorbed by the molecules of rubber and is eventually dissipated as heat. Consequently the rubber gets noticeably hot if we stretch it and un-stretch it repeatedly. The graph of the above type, forming a loop is called hysteresis curve.

Area of the hysteresis loop represents the energy lost.