Elasticity 2: shear modulus
Nico A.M. Schellart, Dept. of Med. Physics, AMC

Principle

The shear modulus or modulus of rigidity (G or sometimes S) is a type of elastic modulus which 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.

Fig. 1 Deformation by shear stress.

, 1)

where F/A is shear stress (force F over cross area A) and Δx/h is shear strain (distance of deformation Δx over height h).

The shear modulus is one of several quantities for measuring the strength of materials. All of them arise in the generalized Hooke's law (see Elasticity and Hooke's law).

Anisotropic materials such as wood and bone are poorly described by elastic moduli.

G and E are related by the Poisson ratio μ (see Elasticity 3: compressibility and bulk modulus).

G = E /(2+μ) 2)

Shear modulus is usually measured in GPa. See Elasticity 1: elastic or Young’s modulus for the values of G of some materials.

Application

G is smaller than E as (2) shows. Therefore, bone fracture mostly occurs when bended or twisted which gives a high shear. In contrast, tendons rupture by tensile stress.

More Info

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.