Rajagopal, K. R.; Srinivasa, A. R. On the thermodynamics of fluids defined by implicit constitutive relations. (English) Zbl 1149.76007 Z. Angew. Math. Phys. 59, No. 4, 715-729 (2008). 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. Cited in 39 Documents MSC: 76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena 76D99 Incompressible viscous fluids 80A17 Thermodynamics of continua Keywords:nonlinear viscous fluids; pressure-dependent viscosity; Bingham materials PDFBibTeX XMLCite \textit{K. R. Rajagopal} and \textit{A. R. Srinivasa}, Z. Angew. Math. Phys. 59, No. 4, 715--729 (2008; Zbl 1149.76007) Full Text: DOI