# Shear modulus (modulus of rigidity)

A material property: the ratio of shear stress to shear strain below the elastic limit. (Also called the modulus of rigidity.)

An isotropic material like aluminum has only one modulus of elasticity. An orthotropic material like titanium has three principal shear moduli.

The shear modulus decreases with temperature.

If other material properties are known and if the material is isotropic, then the shear modulus can be calculated from —

\begin{align} \label{eq:12201a} G &= \frac{E}{2 \, (1 + \nu)} \\[0.7em]%eqn_interline_spacing &= \frac{\rho \, {c_{tw}}^2}{2 \, (1 + \nu)} \nonumber \end{align}

where —

 $$G$$ = shear modulus $$E$$ = modulus of elasticity (Young's modulus) $$\nu$$ = Poisson's ratio $$\rho$$ = density $$c_{tw}$$ = thin-wire wave speed

Also see shear wave.