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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:

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).

Contents 1 Typical values 2 Explanation 3 Relation to Poisson's ratio and Young's modulus 4 See also 5 References

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

Material	Shear modulus (GPa)[1]
Steel	79.3
Copper	63.4
Titanium	41.4
Glass	26.2
Aluminium	25.5
Polyethylene	0.117
Rubber	0.0003

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.

The shear modulus concerns with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences another force (such as friction). In the case of an object that's shaped like a rectangular prism, it will deform into a parallelepiped.

For an isotropic material the relation between shear modulus G and Young's modulus E is

where

G is shear modulus,

E is Young's modulus,

ν is Poisson's ratio.

• Poisson's ratio
• Young's modulus (modulus of elasticity)
• Hooke's law

1. ^ Crandall, Dahl, Lardner (1959). An Introduction to the Mechanics of Solids. McGraw-Hill.