Editing Deformation (engineering) (section)

==Main concepts==
Occurrence of deformation in engineering applications is based on the following background concepts:
* [[Displacement (mechanics)|''Displacements'']] are any change in position of a point on the object, including whole-body translations and rotations ([[rigid transformation]]s).
* [[Deformation (mechanics)|''Deformation'']] are changes in the relative position between internals points on the object, excluding rigid transformations, causing the body to change shape or size. 
* [[Strain (mechanics)|''Strain'']] is the ''relative'' ''internal'' deformation, the [[dimensionless]] change in shape of an infinitesimal cube of material relative to a reference configuration. Mechanical strains are caused by [[Stress (mechanics)|mechanical stress]], ''see [[stress-strain curve]]''.

The relationship between stress and strain is generally linear and reversible up until the [[yield point]] and the deformation is [[Elasticity (physics)|elastic]]. Elasticity in materials occurs when applied stress does not surpass the energy required to break molecular bonds, allowing the material to deform reversibly and return to its original shape once the stress is removed. The linear relationship for a material is known as [[Young's modulus]]. Above the yield point, some degree of permanent distortion remains after unloading and is termed [[Plasticity (physics)|plastic deformation]]. The determination of the stress and strain throughout a solid object is given by the field of [[strength of materials]] and for a structure by [[structural analysis]].

In the above figure, it can be seen that the compressive loading (indicated by the arrow) has caused deformation in the [[cylinder (geometry)|cylinder]] so that the original shape (dashed lines) has changed (deformed) into one with bulging sides. The sides bulge because the material, although strong enough to not crack or otherwise fail, is not strong enough to support the load without change. As a result, the material is forced out laterally. Internal forces (in this case at right angles to the deformation) resist the applied load.