Elastic deformation occurs when an object is stretched or compressed and returns to its original shape and size when the force is removed. No permanent change occurs.
Hooke’s law region
A spring that obeys Hooke’s law deforms elastically. The extension is directly proportional to the applied force:
F = k x
where F is the force in newtons, k is the spring constant in N/m, and x is the extension in metres.
On a force-extension graph, the elastic region is the straight-line section that passes through the origin.
The limit of proportionality
Beyond a certain force, the spring no longer obeys Hooke’s law. The graph starts to curve. The point where this happens is the limit of proportionality.
The elastic limit
The elastic limit is the maximum force (or extension) that the material can withstand and still return to its original length. Beyond the elastic limit, the deformation becomes plastic: the material stays permanently deformed even after the force is removed.
The elastic limit is at or slightly beyond the limit of proportionality.
Energy in elastic deformation
When a spring is stretched elastically, energy is stored in the elastic potential energy store. This energy can be calculated from the area under the force-extension graph. For the linear region:
energy stored = 0.5 x F x x = 0.5 x k x x squared
All of this energy is recovered when the spring returns to its original length. In plastic deformation, some energy is dissipated as thermal energy in the material and is not recovered.
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