Pure shear

An element in pure shear

In mechanics and geology, pure shear is a three-dimensional homogeneous flattening of a body. It is an example of irrotational strain in which a body is elongated in one direction while being shortened perpendicularly. For soft materials, such as rubber, a strain state of pure shear is often used for characterizing hyperelastic and fracture mechanical behavior.

Pure shear stress-strain relation

Pure shear stress, denoted $\tau$, is related to pure shear strain, denoted $\gamma$, by the following equation:

$\tau = \gamma G\,$

where $G$ is the shear modulus of the material, given by

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

Here $E$ is Young's modulus and $\nu$ is Poisson's ratio. Combining gives

$\tau = \frac{\gamma E}{2(1+\nu)}$

See also

• Simple shear