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:
\( {\displaystyle F={\begin{bmatrix}1&\gamma &0\\\gamma &1&0\\0&0&1\end{bmatrix}}} \)
Note that this gives a Green-Lagrange strain of:
\( {\displaystyle E={\frac {1}{2}}{\begin{bmatrix}\gamma ^{2}&2\gamma &0\\2\gamma &\gamma ^{2}&0\\0&0&0\end{bmatrix}}} \)
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:
\( {\displaystyle \epsilon ={\frac {1}{2}}{\begin{bmatrix}0&2\gamma &0\\2\gamma &0&0\\0&0&0\end{bmatrix}}} \)
which has only shearing components.
See also
Simple shear
Squeeze mapping
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.
Hellenica World - Scientific Library
Retrieved from "http://en.wikipedia.org/"
All text is available under the terms of the GNU Free Documentation License
