Abstract
In this paper we study incompressible fluids described by constitutive equations from a different perspective, than that usually adopted, namely that of expressing kinematical quantities in terms of the stress. Such a representation is the appropriate way to express fluids like the classical Bingham fluid or fluids whose material moduli depend on the pressure.
We consider models wherein the symmetric part of the velocity gradient is given by a ""power-law"" of the stress. This stress power-law model automatically satisfies the constraint of incompressibility without our having to introduce a Lagrange multiplier to enforce the constraint.
We compare the stress power-law model with the classical power-law models and we show that the stress power-law model can, for certain parameter values, exhibit qualitatively different response characteristics than the classical power-law models and-on the other hand-it can be, for certain parameter values, used as a substitute for the classical power-law models.