Simple Shear in Solid Mechanics
In solid mechanics, a simple shear deformation is defined as an isochoric plane deformation in which there are a set of line elements with a given reference orientation that do not change length and orientation during the deformation. This deformation is differentiated from a pure shear by virtue of the presence of a rigid rotation of the material.
If is the fixed reference orientation in which line elements do not deform during the deformation and is the plane of deformation, then the deformation gradient in simple shear can be expressed as
We can also write the deformation gradient as
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