Angular Deformation

Our previous discussion of rotation also leads to the definition of angular deformation or rate of shear strain. For a two-dimensional flow this is given by,

$$\dot \gamma = {d\alpha \over {dt}} + {d\beta \over {dt}} = {\partial v\over {\partial x}} + {\partial u \over {\partial y}}$$ (4.43)

Shear stress for the element is thus given by

$$\tau_{xy}= \mu \dot\gamma =  \mu \left( {\partial v\over {\partial x}} + {\partial u \over {\partial y}}\right)$$ (4.44)

(c) Aerospace, Mechanical & Mechatronic Engg. 2005
University of Sydney