Strain

From Academic Kids

A separate article is titled strain (biology).
For an account the manga series, see Strain (manga).

In any branch of science dealing with materials and their behaviour, strain is the geometrical expression of deformation caused by the action of stress on a physical body. Strain therefore expresses itself as a change in size and/or shape. In the case of geological action of the earth, if the release of stress through strain in rocks is sufficiently large, earthquakes may occur.

If strain is equal over all parts of the body, it is referred to as homogeneous strain; otherwise, it is inhomogeneous strain.

Strain in the Earth resulting from stresses across faults results in motion over the fault surface and a combination of brittle and ductile deformation of the surrounding rocks. Brittle strain is exhibited as fractures, faults and other discontinuous breaks in the fabric of the rock. Ductile strain occurs as shear zones, flow bands and folding.

Quantifying strain

Given that strain results in the deformation of a body, it can be measured by calculating the change in length of a line or by the change in angle between two lines (where these lines are theoretical constructs within the deformed body). The change in length of a line is termed the stretch and may be given by

<math>e={l \over l_0}<math>

where

l is the change in length
l0 is the original undeformed length

If e is positive, the body has been lengthened; if it is negative, it has been compressed.

This equation is commonly used to calculate the beta factor for lithospheric extension during the formation of sedimentary basins.

In structural engineering the (relative) strain is given as:

<math>\varepsilon = \frac {\Delta_l} {l_0} (*100%)<math>

where

ε = unitless measure of engineering strain;
Δl = deformation elongation or change in length; and
l0 = the original length before any load is applied.

This definition is only valid for small deformation. Imagine a body is deformed twice, first by Δl1 then by Δl2 (cumulative deformation). The final strain

<math>\varepsilon = \frac{\Delta l_1 + \Delta l_2}{l_0}<math>

is slightly different from the sum of the strains :

<math>\varepsilon_1 = \frac{\Delta l_1}{l_0}<math>

and

<math>\varepsilon_2 = \frac{\Delta l_2}{l_0 + \Delta l_1}<math>

As long as Δl1 << l0, it is possible to write:

<math>\varepsilon_2 \simeq \frac{\Delta l_2}{l_0}<math>

and thus

<math>\varepsilon = \varepsilon_1 + \varepsilon_2<math>

This is no longer possible for great deformation.

In case of great deformation, the strain is defined by:

<math>d\varepsilon = \frac{dl}{l}<math>

and thus

<math>\varepsilon = \ln \left (\frac{l}{l_0} \right )<math>

It is easy to see that the small deformation formula is the series expansion of the general formula.

See also

sl:relativni raztezek nl:rek

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