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.

[1]  D. Dowson,et al.  Elasto-hydrodynamic lubrication : the fundamentals of roller and gear lubrication , 1966 .

[2]  E. G.,et al.  The Physics of High Pressure , 1933, Nature.

[3]  K. Rajagopal,et al.  Review of the uses and modeling of bitumen from ancient to modern times , 2003 .

[4]  Peter A. Kottke,et al.  Pressure-Viscosity Relationships for Elastohydrodynamics , 2003 .

[5]  Leonard Eugene Dickson,et al.  A Theory of Invariants , 1909 .

[6]  E. Andrade,et al.  Viscosity of Liquids. , 1931, Nature.

[7]  Andras Z. Szeri,et al.  Fluid Film Lubrication: Theory and Design , 1998 .

[8]  Percy Williams Bridgman,et al.  The Effect of Pressure on the Viscosity of Forty-Three Pure Liquids , 1926 .

[9]  Carl Barus,et al.  Isothermals, isopiestics and isometrics relative to viscosity , 1893, American Journal of Science.

[10]  R.N.J. Saal,et al.  CHAPTER 9 – RHEOLOGICAL PROPERTIES OF ASPHALTS , 1958 .

[11]  J. Frenkel.  The Viscosity of Liquids. , 1930, Nature.

[12]  C. Truesdell,et al.  The Nonlinear Field Theories in Mechanics , 1968 .

[13]  Arun R. Srinivasa,et al.  On the nature of constraints for continua undergoing dissipative processes , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[14]  K. R. Rajagopal,et al.  Simple flows of fluids with pressure–dependent viscosities , 2001, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[15]  Erik Höglund,et al.  Influence of lubricant properties on elastohydrodynamic lubrication , 1999 .

[16]  E. C. Bingham,et al.  The Alternating Stress Method for the Measurement of the Consistency of Very Stiff Materials , 1934 .

[17]  C. F. Gauss,et al.  Über Ein Neues Allgemeines Grundgesetz der Mechanik , 1829 .