Shear modulus

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In materials science, shear modulus, G, or sometimes S or μ, sometimes referred to as the modulus of rigidity, is defined as the ratio of shear stress to the shear strain:

<math>G \ \stackrel{\mathrm{def}}{=}\ \frac{F/A}{\Delta x/h} = \frac{F h}{\Delta x A}</math>

where F/A is shear stress and Δx/h is shear strain.

Shear modulus is usually measured in GPa (gigapascals) or ksi (thousands of pounds per square inch).

1 Typical values
2 Explanation
3 See also
4 References

[edit] Typical values

The following are values of the shear modulus for select isotropic materials at room temperature:

Material	Shear modulus (GPa)<ref name=CDL>Crandall, Dahl, Lardner (1959). An Introduction to the Mechanics of Solids. McGraw-Hill.</ref>
Steel	79.3
Copper	63.4
Titanium	41.4
Glass	26.2
Aluminum	25.5
Polyethylene	0.117
Rubber	0.0003

[edit] 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. Anisotropic materials such as wood and paper exhibit differing material response to stress or strain when tested in different directions.

In solids, there are two kinds of sound waves, pressure waves and shear waves. The speed of sound for shear waves is controlled by the shear modulus.