# Simple shear

In fluid mechanics, **simple shear** is a special case of deformation where only one component of velocity vectors has a non-zero value:

And the gradient of velocity is constant and perpendicular to the velocity itself:

- ,

where is the shear rate and:

The displacement gradient tensor Γ for this deformation has only one nonzero term:

Simple shear with the rate is the combination of pure shear strain with the rate of 1/2 and rotation with the rate of 1/2:

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.^{[1]} This deformation is differentiated from a **pure shear** by virtue of the presence of a rigid rotation of the material.

If **e**_{1} is the fixed reference orientation in which line elements do not deform during the deformation and **e**_{1} − **e**_{2} is the plane of deformation, then the deformation gradient in simple shear can be expressed as

We can also write the deformation gradient as

## See also

## References

- ↑ Ogden, R. W. (1984).
*Non-Linear Elastic Deformations*. Dover.