Simple Shear

Simple Shear is a special case of Deformation of a fluid where only one component of Velocity vectors has a non-zero value:

V_x=f(x,y)

V_y=V_z=0

And the Gradient of velocity is perpendicular to it:

rac {\partial V_x} {\partial y} = \dot \gamma

,

where

\dot \gamma

is the Shear Rate and:

rac {\partial V_x} {\partial x} = rac {\partial V_x} {\partial z} = 0

\Gamma

for this deformation has only one non-zero term:

\Gamma = \begin{bmatrix} 0 & {\dot \gamma} & 0 \  0 & 0 & 0 \ 0 & 0 & 0 \end{bmatrix}

Simple shear with the rate

\dot \gamma

is the combination of Pure Shear Strain with the rate of

\dot \gamma \over 2

and Rotation with the rate of

\dot \gamma \over 2

\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}

An important example of simple shear is Laminar flow through long channels of constant cross-section ( Poiseuille Flow ).

	CATEGORIES ABOUT SIMPLE SHEAR

	fluid mechanics

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