Pure shear

An element in 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 a body is elongated in one direction while being shortened perpendicularly.^[2] For soft materials, such as rubber, a strain state of pure shear is often used for characterizing hyperelastic and fracture mechanical behavior. ^{[3] [4]}

Pure shear stress-strain relation

Pure shear stress, denoted $\tau$, is related to pure shear strain, denoted $\gamma$, by the following equation:^[5]

$\tau = \gamma G\,$

where $G$ is the shear modulus of the material, given by

$G = \frac{E}{2(1+\nu)}$

Here $E$ is Young's modulus and $\nu$ is Poisson's ratio. Combining gives

$\tau = \frac{\gamma E}{2(1+\nu)}$

See also

• Simple shear

References

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. "Pure shear". Answers.com. Retrieved 24 December 2011.
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. "Strength of Materials". Eformulae.com. Retrieved 24 December 2011.