## On the thermodynamics of fluids defined by implicit constitutive relations.(English)Zbl 1149.76007

Summary: We develop a thermodynamically consistent theory for describing the response of nonlinear viscous fluids whose constitutive equations are of the form $$\mathbf{f (T, D)} = 0$$. 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.

### MSC:

 76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena 76D99 Incompressible viscous fluids 80A17 Thermodynamics of continua
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