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:
F=\begin{bmatrix}1&\gamma&0\\\gamma&1&0\\0&0&1\end{bmatrix}
Note that this gives a Green-Lagrange strain of:
E=
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\begin{bmatrix}\gamma2&2\gamma&0\\2\gamma&\gamma2&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:
\epsilon=
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\begin{bmatrix}0&2\gamma&0\\2\gamma&0&0\\0&0&0\end{bmatrix}
which has only shearing components.