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{{comicsproj
[[Image:Shear scherung.svg|thumb|right|Shear strain]]
|class=start
In [[materials science]], '''shear modulus''' or '''modulus of rigidity''', denoted by ''G'', or sometimes ''S'' or ''μ'', is defined as the ratio of [[shear stress]] to the [[shear strain]]:<ref>{{GoldBookRef|title=shear modulus, ''G''|file=S05635}}</ref>
<!-- B-Class checklist -->
:<math>G \ \stackrel{\mathrm{def}}{=}\ \frac {\sigma_{xy}} {\epsilon_{xy}} = \frac{F/A}{\Delta x/I} = \frac{F I}{\Delta x A} </math>
<!-- 1. It is suitably referenced, and all major points are appropriately cited. -->

|B-Class-1=no
where
<!-- 2. It reasonably covers the topic, and does not contain major omissions or inaccuracies. -->
:<math>\sigma_{xy} = F/A \,</math> = shear stress;
|B-Class-2=no
:<math>F</math> is the force which acts
<!-- 3. It has a defined structure, including a lead section and one or more sections of content. -->
:<math>A</math> is the area on which the force acts
|B-Class-3=yes
:<math>\epsilon_{xy} = \Delta x/I = \tan \theta \,</math> = shear strain;
<!-- 4. It is free from major grammatical errors. -->
:<math>\Delta x</math> is the transverse displacement
|B-Class-4=yes
:<math>I</math> is the initial length
<!-- 5. It contains appropriate supporting materials, such as an infobox, images, or diagrams. -->

|B-Class-5=yes
Shear modulus is usually measured in GPa ([[Pascal (unit)|gigapascal]]s) or ksi (thousands of pounds per square inch).
|importance=Low

|DC-work-group=yes
{| class="wikitable" align=right
}}
!Material
!Typical values for <br>shear modulus ([[Giga|G]][[Pascal (unit)|Pa]])<br> <small>(at room temperature)</small>
|-
|[[Diamond]]<ref name=McSkimin>{{cite Journal|last=McSkimin|first=H.J.|coauthors=Andreatch, P.
|date = 1972|title=Elastic Moduli of Diamond as a Function of Pressure and Temperature|journal = J. Appl. Phys.|volume = 43|pages=2944–2948|doi=10.1063/1.1661636}}</ref>
|478.
|-
|[[Steel]]<ref name=CDL>{{cite book|author=Crandall, Dahl, Lardner|title=An Introduction to the Mechanics of Solids|publisher=McGraw-Hill|city=Boston|year=1959}}</ref>
|79.3
|-
|[[Copper]]<ref>[http://homepages.which.net/~paul.hills/Materials/MaterialsBody.html Material properties]</ref>
|44.7
|-
|[[Titanium]]<ref name=CDL/>
|41.4
|-
|[[Glass]]<ref name=CDL/>
|26.2
|-
|[[Aluminium]]<ref name=CDL/>
|25.5
|-
|[[Polyethylene]]<ref name=CDL/>
|0.117
|-
|[[Rubber]]<ref name=Spanos>{{cite Journal|last=Spanos|first=Pete|year=2003|title=Cure system effect on low temperature dynamic shear modulus of natural rubber
|journal = Rubber World|month=November|url=http://www.thefreelibrary.com/Cure+system+effect+on+low+temperature+dynamic+shear+modulus+of...-a0111451108}}</ref>
|0.0006
|}

== Explanation ==

The shear modulus is one of several quantities for measuring the strength of materials. All of them arise in the generalized [[Hooke's law]]:
* [[Young's modulus]] describes the material's response to linear strain (like pulling on the ends of a wire),
* the [[bulk modulus]] describes the material's response to uniform [[pressure]], and
* the '''shear modulus''' describes the material's response to shearing strains.

The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force (such as friction). In the case of an object that's shaped like a rectangular prism, it will deform into a [[parallelepiped]]. [[Anisotropic]] materials such as [[wood]] and [[paper]] exhibit differing material response to stress or strain when tested in different directions. In this case, when the deformation is small enough so that the deformation is linear, the elastic moduli, including the shear modulus, will then be a tensor, rather than a single scalar value.

[[Image:SpiderGraph ShearModulus.GIF|250px|thumb|Influences of selected [[glass]] component additions on the shear modulus of a specific base glass.<ref>[http://www.glassproperties.com/shear_modulus/ Shear modulus calculation of glasses]</ref>]]

==Waves==
In homogeneous and [[isotropic]] solids, there are two kinds of waves, [[P wave|pressure waves]] and [[S wave|shear waves]]. The velocity of a shear wave, <math>(v_s)</math> is controlled by the shear modulus,
:<math>v_s = \sqrt{\frac {G} {\rho} }</math>
where
:G is the shear modulus
:<math>\rho</math> is the solid's [[density]].

==See also==
* [[Shear strength]]
* [[Dynamic modulus]]
* [[Hooke's law]]
* [[Impulse excitation technique]]

==References==
{{reflist}}

{{Elastic moduli}}

[[Category:Materials science]]
[[Category:Elasticity (physics)]]

[[da:Forskydningsmodul]]
[[de:Schubmodul]]
[[es:Módulo de elasticidad transversal]]
[[fr:Module de cisaillement]]
[[ko:전단 탄성 계수]]
[[it:Modulo di taglio]]
[[he:מודול הגזירה]]
[[nl:Schuifmodulus]]
[[ja:剛性率]]
[[pl:Moduł Kirchhoffa]]
[[pt:Módulo de cisalhamento]]
[[sl:Strižni modul]]
[[sv:Skjuvmodul]]
[[th:โมดูลัสของแรงเฉือน]]
[[uk:Модуль зсуву]]
[[zh:剪切模量]]

Revision as of 14:20, 12 October 2008

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