The stretch ratio is a measure of the extensional or normal strain of a differential line element, which can be defined at either the undeformed configuration or the deformed configuration.
The stretch ratio for the differential element (Figure) in the direction of the unit vector at the material point, in the undeformed configuration, is defined as
where is the deformed magnitude of the differential element .
Similarly, the stretch ratio for the differential element (Figure), in the direction of the unit vector at the material point, in the deformed configuration, is defined as
The normal strain in any direction can be expressed as a function of the stretch ratio,
This equation implies that the normal strain is zero, i.e. no deformation, when the stretch is equal to unity. Some materials, such as elastometers can sustain stretch ratios of 3 or 4 before they fail, whereas traditional engineering materials, such as concrete or steel, fail at much lower stretch ratios, perhaps of the order of 1.001 (reference?)
Read more about this topic: Finite Strain Theory
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