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And the gradient of velocity is constant and perpendicular to the velocity itself:
where is the shear rate and:
The deformation gradient tensor for this deformation has only one non-zero term:
Important examples of simple shear include laminar flow through long channels of constant cross-section (Poiseuille flow), and elastomeric bearing pads in base isolation systems to allow critical buildings to survive earthquakes undamaged.
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
- Ogden, R. W., 1984, Non-linear elastic deformations, Dover.
- "Where do the Pure and Shear come from in the Pure Shear test?" (PDF). Retrieved 12 April 2013.
- "Comparing Simple Shear and Pure Shear" (PDF). Retrieved 12 April 2013.