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 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.

See also



  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. ^ 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.
  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.