Shear modulus

An important elastic modulus, also known as rigidity or the modulus of rigidity, or the second Lamé parameter. Symbolized as &mu; or sometimes G.

Definition
The ratio of shear stress to shear strain:


 * $$\mathrm{shear}\ \mathrm{modulus} = \frac{\mathrm{shear}\ \mathrm{stress}}{\mathrm{shear}\ \mathrm{strain}}$$


 * $$\mu = \frac{F/WL}{\tan \theta} = \frac{F/WL}{\Delta L / L}$$

Other expressions
Shear modulus can be expressed in terms of elastic properties:


 * $$\mu = \frac{E}{2(1+\nu)}$$

And it can be expressed in terms of acoustic properties:


 * $$\mu = \rho V_\mathrm{S}^2$$

from which it follows that


 * $$\mu\rho = I_\mathrm{S}^2$$

where I S is shear impedance and &rho; is density.

Typical values
Usually about 3 &times; 1010 Pa.