Elastic modulus
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209704602
2008-05-02T14:57:32Z
Berland
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[[WP:UNDO|Undid]] revision 209696258 by [[Special:Contributions/122.107.18.211|122.107.18.211]] ([[User talk:122.107.18.211|talk]])
An '''elastic modulus''', or '''modulus of elasticity''', is the mathematical description of an object or substance's tendency to be deformed elastically (i.e., non-permanently) when a [[force]] is applied to it. The elastic modulus of an object is defined as the [[slope]] of its [[stress-strain curve]] in the elastic deformation region:
:<math>\lambda \ \stackrel{\text{def}}{=}\ \frac {\text{stress}} {\text{strain}}</math>
where <var>λ</var> (lambda) is the elastic modulus; <var>[[stress (physics)|stress]]</var> is the force causing the deformation divided by the area to which the force is applied; and <var>[[strain (materials science)|strain]]</var> is the ratio of the change caused by the stress to the original state of the object. If stress is measured in [[pascal (unit)|pascal]]s, since strain is a unitless ratio, then the units of <var>λ</var> are pascals as well. An alternative definition is that the elastic modulus is the stress required to cause a sample of the material to double in length. This is not realistic for most materials because the value is far greater than the yield stress of the material or the point where elongation becomes nonlinear, but some may find this definition more intuitive.
Specifying how stress and strain are to be measured, including directions, allows for many types of elastic moduli to be defined.
The three primary ones are
* ''[[Young's modulus]]'' (<var>E</var>) describes tensile [[Elasticity (physics)|elasticity]], or the tendency of an object to deform along an axis when opposing forces are applied along that axis; it is defined as the ratio of [[tensile stress]] to [[tensile]] [[Strain (materials science)|strain]]. It is often referred to simply as the ''elastic modulus''.
* The ''[[shear modulus]]'' or ''modulus of rigidity'' (<var>G</var> or <math>\mu</math>) describes an object's tendency to shear (the deformation of shape at constant volume) when acted upon by opposing forces; it is defined as [[shear stress]] over [[shear strain]]. The shear modulus is part of the derivation of [[viscosity]].
* The ''[[bulk modulus]]'' (<var>K</var>) describes volumetric elasticity, or the tendency of an object's volume to deform when under pressure; it is defined as [[Stress (physics)#Stress deviator tensor|volumetric stress]] over volumetric strain, and is the inverse of [[compressibility]]. The bulk modulus is an extension of Young's modulus to three dimensions.
Three other elastic moduli are [[Poisson's ratio]], [[Lamé's first parameter]], and [[P-wave modulus]].
Homogeneous and [[isotropic]] (similar in all directions) materials (solids) have their (linear) elastic properties fully described by two elastic moduli, and one may choose any pair. Given a pair of elastic moduli, all other elastic moduli can be calculated according to formulas in the table below.
[[Inviscid fluids]] are special in that they cannot support shear stress, meaning that the shear modulus is always zero. This also implies that [[Young's modulus]] is always zero.
{{Elastic moduli}}
==See also==
* [[Stiffness]]
* [[Elastic limit]]
* [[Elasticity (physics)]]
* [[Impulse excitation technique]]
* [[Tensile strength]]
* [[Elastic wave]]
* [[Dynamic modulus]]
* [[Transverse isotropy]]
{{classicalmechanics-stub}}
[[Category:Materials science]]
[[Category:Elasticity (physics)]]
==External links==
*[http://www.matweb.com Free database of engineering properties for over 63,000 materials]
[[es:Constante elástica]]
[[he:מודול הנפח]]
[[ja:弾性率]]
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[[simple:Elastic modulus]]
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