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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 there is no rotation occurring, which can be seen from the equal off-diagonal components of the strain tensor. The linear approximation to the Green-Lagrange strain shows that the small strain tensor is:

which has only shearing components.

**^**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. Bibcode:2001PRC....30..389Y. doi:10.1179/146580101101541787. S2CID 136628719.**^**"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.