On implicit constitutive theories for fluids

We consider generalizations of fluid models wherein the fluid is assumed to be incompressible, but with the viscosity depending on the pressure. We show that a natural setting for the development of such models is a class of implicit constitutive relations, which, in addition to the fluid model described here, provides a means for developing other complex models for viscoelastic fluids which cannot be set within the ambit of classical explicit constitutive relations for the stress in terms of the histories of appropriate kinematical variables.