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]

If $\lambda$ is the stretch ratio applied to the material, then the deformation gradient in pure shear can be expressed as^[5]

{\boldsymbol {F}}={\begin{bmatrix}\lambda &0&0\\0&1&0\\0&0&1/\lambda \end{bmatrix}}.

The linear elastic stress-strain law for the case of pure shear is:

{\begin{bmatrix}\sigma _{11}\\\sigma _{22}\\\sigma _{12}\end{bmatrix}}\,=\,{\begin{bmatrix}\sigma \\\nu \sigma \\0\end{bmatrix}}\,=\,{\frac {E}{1-\nu ^{2}}}{\begin{bmatrix}1&\nu &0\\\nu &1&0\\0&0&{\frac {1-\nu }{2}}\end{bmatrix}}{\begin{bmatrix}\varepsilon _{11}\\0\\0\end{bmatrix}}

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.
↑ Moreira, D.C.; Nunes, L.C.S. (April 2013). "Comparison of simple and pure shear for an incompressible isotropic hyperelastic material under large deformation". Polymer Testing. 32 (2): 240–248. doi:10.1016/j.polymertesting.2012.11.005.

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[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. doi:10.1179/146580101101541787.

[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.

[5] Moreira, D.C.; Nunes, L.C.S. (April 2013). "Comparison of simple and pure shear for an incompressible isotropic hyperelastic material under large deformation". Polymer Testing. 32 (2): 240–248. doi:10.1016/j.polymertesting.2012.11.005.

Pure shear

See also

References