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 deformation gradient tensor for this deformation has only one non-zero term:

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

\Gamma = \begin{matrix} \underbrace \begin{bmatrix} 0 & {\dot \gamma} & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} \\ \mbox{simple shear}\end{matrix} = \begin{matrix} \underbrace \begin{bmatrix} 0 & {\dot \gamma \over 2} & 0 \\ {\dot \gamma \over 2} & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} \\ \mbox{pure shear} \end{matrix} + \begin{matrix} \underbrace \begin{bmatrix} 0 & {\dot \gamma \over 2} & 0 \\ {- { \dot \gamma \over 2}} & 0 & 0 \\ 0 & 0 & 0 \end{bmatrix} \\ \mbox{solid rotation} \end{matrix}

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.

Read more about Simple Shear:  Simple Shear in Solid Mechanics, See Also

Famous quotes containing the word simple:

    “Well, I had gone and spoiled it again, made another mistake. A double one in fact. There were plenty of ways to get rid of that officer by some simple and plausible device, but no, I must pick out a picturesque one; it is the crying defect of my character.”
    —Mark Twain [Samuel Langhorne Clemens] (1835–1910)