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:

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