Pure shear

{{Use dmy dates|date=November 2017}}

In mechanics and geology, pure shear is a three-dimensional homogeneous flattening of a body.{{cite web|url=http://www.geology.sdsu.edu/visualstructure/vss/htm_hlp/pure_s.htm|title=Definition and Mathematics of Pure Shear|last=Reish|first=Nathaniel E.|author2=Gary H. Girty |publisher=San Diego State University Department of Geological Sciences|access-date=24 December 2011}} 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.{{cite journal|last1=Yeoh|first1=O. H.|title=Analysis of deformation and fracture of 'pure shear'rubber testpiece|journal=Plastics, Rubber and Composites|date=2001|volume=30|issue=8|pages=389–397|doi=10.1179/146580101101541787|bibcode=2001PRC....30..389Y |s2cid=136628719 }} Pure shear is differentiated from simple shear in that pure shear involves no rigid body rotation. {{cite web|url=http://www.endurica.com/wp-content/uploads/2015/06/Pure-Shear-Nomenclature.pdf|title=Where do the Pure and Shear come from in the Pure Shear test?|access-date=12 April 2013}}{{cite web|url=http://www.endurica.com/wp-content/uploads/2015/06/Comparing-Pure-Shear-and-Simple-Shear.pdf|title=Comparing Simple Shear and Pure Shear|access-date=12 April 2013}}

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.