Abstract: A generalized viscosity model was proposed for generalized Newtonian fluids, which was expressed as a function of the invariants of stress and strain rate tensors. Assuming the independency of the second and third invariants of the rate of strain tensor, this model described well various shear and extensional as well as complex flows. When applied to steady-state simple or extensional flows, the obtained viscosities were agree with those traditionally defined.

Key words: shear and extensional viscosities, generalized viscosity, the independence of viscosity on the second and the third invariants of the rate of strain tensor (deformation), the second invariant of the extra-stress tensor, and the uniqueness of viscosity.