On the thermodynamics of fluids defined by implicit constitutive relations

In this paper, we develop a thermodynamically consistent theory for describing the response of nonlinear viscous fluids whose constitutive equations are of the form f (T, D) = 0. We show that such constitutive equations which include classical constitutive equations wherein the stress is expressed explicitly in terms of the kinematical quantities, provide a rich class of physically meaningful fluid response functions which allows us to describe a wider range of material behavior, including that of a general class of incompressible fluids, incompressible fluids with pressure dependent viscosity, and Bingham (or pseudoplastic) materials.