What is "shear modulus"

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:

$$G \ \stackrel{\mathrm{def}}{=}\ \frac {\tau_{xy}} {\gamma_{xy}} = \frac{F/A}{\Delta x/l} = \frac{F l}{A \Delta x}$$

where

τ = F/A 
= shear stress;

F
is the force which acts

A
is the area on which the force acts

in engineering, γ = Δx/l = tanθ  = shear strain. Elsewhere, γ = θ Δx is the transverse displacement l is the initial length

Shear modulus' derived SI unit is the pascal (Pa), although it is usually expressed in gigapascals (GPa) or in thousands of pounds per square inch (ksi). Its dimensional form is MLT, replacing force by mass times acceleration.

The shear modulus is always positive.