Pure shear

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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[edit]

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[edit]


  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.