 Simple Shear

# Simple shear

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

[itex] V_x=f(x,y)[/itex]

[itex] V_y=V_z=0[/itex]

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

[itex]frac = dot gamma [/itex],

where [itex]dot gamma [/itex] is the shear rate and:

[itex]frac = frac = 0 [/itex]

The deformation gradient tensor [itex]Gamma[/itex] for this deformation has only one non-zero term:

[itex]Gamma = begin 0 & & 0 \ 0 & 0 & 0 \ 0 & 0 & 0 end[/itex]

Simple shear with the rate [itex]dot gamma[/itex] is the combination of pure shear strain with the rate of [itex]dot gamma over 2[/itex] and rotation with the rate of [itex]dot gamma over 2[/itex]:

[itex]Gamma =begin underbrace begin 0 & & 0 \ 0 & 0 & 0 \ 0 & 0 & 0 end\ mboxend =begin underbrace begin 0 & & 0 \ & 0 & 0 \ 0 & 0 & 0 end \ mbox end+ begin underbrace begin 0 & & 0 \ & 0 & 0 \ 0 & 0 & 0 end \ mbox end [/itex]

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.

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