# Pure shear

In mechanic and geology, pure shear is a three-dimensional homogeneous flattening of a body.[1] It is an example of irrotational strain in which body is elongated in one direction while being shortened perpendicularly.[2] For soft materials, such as rubber, a strain state of pure shear is often used for characterizing hyperelastic and fracture mechanical behaviour.[3] [4] [5] A rod under torsion is a practical example for a body under pure shear.

## Pure shear stress-strain relation

Pure shear stress, denoted ${\displaystyle \tau }$, is related to pure shear strain, denoted ${\displaystyle \gamma }$, by the following equation:[6]

${\displaystyle \tau =\gamma G\,}$

where ${\displaystyle G}$ is the shear modulus of the material, given by

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

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

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