# Pure shear

An element in pure shear

In mechanics and geology, pure shear is a three-dimensional homogeneous flattening of a body.[1] It is an example of irrotational strain in which a 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 behavior. [3] [4]

## Pure shear stress-strain relation

Pure shear stress, denoted ${\displaystyle \tau }$, is related to pure shear strain, denoted ${\displaystyle \gamma }$, by the following equation:[5]

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

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

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

## References

1. ^ Reish, Nathaniel E.; Gary H. Girty. "Definition and Mathematics of Pure Shear". San Diego State University Department of Geological Sciences. Retrieved 24 December 2011.
2. ^ "Pure shear". Answers.com. Retrieved 24 December 2011.
3. ^ "Where do the Pure and Shear come from in the Pure Shear test?" (PDF). Retrieved 12 April 2013.
4. ^ "Comparing Simple Shear and Pure Shear" (PDF). Retrieved 12 April 2013.
5. ^ "Strength of Materials". Eformulae.com. Retrieved 24 December 2011.