Simple shear is a deformation in which parallel planes in a material remain parallel and maintain a constant distance, while translating relative to each other.
In fluid mechanics In fluid mechanics, simple shear is a special case of deformation where only one component of velocity vectors has a non-zero value:
V x = f ( x , y ) {\displaystyle V_{x}=f(x,y)}
V y = V z = 0 {\displaystyle V_{y}=V_{z}=0}
And the gradient of velocity is constant and perpendicular to the velocity itself:
∂ V x ∂ y = γ ˙ {\displaystyle {\frac {\partial V_{x}}{\partial y}}={\dot {\gamma }}} , where γ ˙ {\displaystyle {\dot {\gamma }}} is the shear rate and:
∂ V x ∂ x = ∂ V x ∂ z = 0 {\displaystyle {\frac {\partial V_{x}}{\partial x}}={\frac {\partial V_{x}}{\partial z}}=0}
The displacement gradient tensor Γ for this deformation has only one nonzero term:
Γ = [ 0 γ ˙ 0 0 0 0 0 0 0 ] {\displaystyle \Gamma ={\begin{bmatrix}0&{\dot {\gamma }}&0\\0&0&0\\0&0&0\end{bmatrix}}}
Simple shear with the rate γ ˙ {\displaystyle {\dot {\gamma }}} is the combination of pure shear strain with the rate of 1/2 γ ˙ {\displaystyle {\dot {\gamma }}} and rotation with the rate of 1/2 γ ˙ {\displaystyle {\dot {\gamma }}} :
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