# 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 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 behaviour.[2] Pure shear is differentiated from simple shear in that pure shear involves no rigid body rotation. [3][4]

The deformation gradient for pure shear is given by:

Note that this gives a Green-Lagrange strain of:

Here we note that there is no rotation occurring which can be seen from the equal off-diagonal components of the strain tensor. It is also worth noting that if we take the linear approximation to the Green-Lagrange strain we see that the small strain tensor is:

Which has only shearing components.

## See also

## References

- Reish, Nathaniel E.; Gary H. Girty. "Definition and Mathematics of Pure Shear". San Diego State University Department of Geological Sciences. Retrieved 24 December 2011.
- Yeoh, O. H. (2001). "Analysis of deformation and fracture of 'pure shear'rubber testpiece".
*Plastics, Rubber and Composites*.**30**(8): 389–397. doi:10.1179/146580101101541787. - "Where do the Pure and Shear come from in the Pure Shear test?" (PDF). Retrieved 12 April 2013.
- "Comparing Simple Shear and Pure Shear" (PDF). Retrieved 12 April 2013.