Strain (mechanics)

Strain is the relative deformation of a material, expressed as a change in dimension or shape compared with an original or reference state. It is dimensionless and may vary across a material.

Engineering strain: Change in length divided by the original length of a material segment. This simple measure matches the usual definition of strain for uniaxial stretching.
Displacement field: A function assigning each material point its displacement from a reference position. Spatial changes in displacement produce local strain.
Stress–strain curve: A graph relating stress to strain during a material test. Its shape reveals stiffness, yielding, and failure as strain increases.
Stress (mechanics): Internal force per unit area within a material, represented by a tensor in continuum mechanics. Stress describes internal loading, while strain describes the resulting deformation.
True strain: The integral of incremental length changes divided by the length at each increment during deformation. It accounts for changing dimensions during large extensions, unlike engineering strain.
Deformation gradient: A tensor mapping infinitesimal vectors in a reference configuration to their deformed counterparts. It provides the local geometric data from which finite strain measures are built.
Strain gauge: A sensor that infers strain from changes in electrical resistance or another measurable property. It turns small structural deformations into measurable signals.
Rigid-body motion: Translation and rotation of a body without changes in distances between its points. Rigid-body motion changes position but produces no strain.
Shear strain: A measure of angular distortion caused by tangential deformation. It describes shape change that lengthwise strain alone cannot represent.
Reference configuration: The chosen initial or comparison state of a body used to describe its deformation. Strain depends on comparing the current state with a specified reference.

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