Deformations and elasticity

Deformable objects

Under the appropriate conditions, virtually all objects are deformable: external forces can change their shape or their physical dimensions.

Note that a single force will not likely deform an object – sooner will it cause it to accelerate. Deformation requires a more complex arrangement of forces: at its simplest, a pair of forces equal in magnitude but opposite in direction, keeping the object in place but pulling its different regions apart. In such cases, we consider the magnitude of only one force out of the pair as the measure of the deforming effect.

Elastic v plastic objects

Elastic objects

Objects that revert to their original shape and size after the deforming forces cease to act are called elastic.

Note that no matter their substance, most objects can be regarded as elastic within certain limits of deformation (elastic limit). For example, a windowpane might vibrate elastically if the amplitude of the vibrations is small.

Plastic objects

We call an object plastic if it stays permanently altered in shape and size even after the deforming forces have ceased to act.

Note that sufficiently large deformations will leave all objects permanently altered, regardless of their substance.

Depending on the direction of the force relative to the object, deformations can be of different types. These require slightly different treatment.

Tension

When the force acts in a direction perpendicular to that of the surface being displaced, we call the deformation tension. In this case, one dimension (for instance, the length) of the object changes, whilst the shape stays about the same.

Shearing

A force acting parallel to the surface being displaced will cause a deformation called shearing. Here the dimensions will stay roughly the same and the shape of the object will change.

Volume deformations

Forces of uniform magnitude acting in directions perpendicular to the surfaces of the object (see the figure) will cause deformations which keep the shape of the object whilst changing all dimensions simultaneously in approximately the same ratio.

Torsion

https://commons.wikimedia.org/wiki/File:Angle_torsion_cylindre.svg (CC BY-SA)

A torque acting on an object stopped from rotating by an oppositely directed torque might cause a twist in it. We call this type of deformation torsion.