On the development of fluid models of the differential type within a new thermodynamic framework. (English) Zbl 1258.76024

Summary: We assess the status of a fluid of grade two within the context of a new thermodynamic framework that has been put into place that appeals to the maximization of the rate of entropy production for making a choice of constitutive equations from an admissible set. Unlike fluid of the rate type like the Maxwell fluid, the Oldroyd-B fluid or Burgers’ fluid, we see that certain modifications need to be made if we have to accommodate differential type fluids such as fluids of grade two.


76A05 Non-Newtonian fluids
80A17 Thermodynamics of continua
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[1] De Groot, S. R.; Mazur, P.: Non-equilibrium thermodynamics, (1962) · Zbl 1375.82003
[2] Dunn, J. E.; Fosdick, R. L.: Thermodynamics, stability, and boundedness of fluids of complexity 2 and fluids of second grade, Arch. rational mech. Anal. 56, 191-252 (1974) · Zbl 0324.76001
[3] Dunn, J. E.; Rajagopal, K. R.: Fluids of differential type: critical review and thermodynamic analysis, Int. J. Eng. sci. 33, 689-729 (1995) · Zbl 0899.76062
[4] Eckart, C.: The thermodynamics of irreversible processes IV. The theory of elasticity and anelasticity, Phys. rev. 73, 373-382 (1948) · Zbl 0032.22201
[5] Eshelby, J. D.: The continuum theory of lattice defects, Solid state physics 3, 79-144 (1956)
[6] Fosdick, R. L.; Rajagopal, K. R.: Anomalous features in the model of second order fluids, Archive ration. Mech. anal. 70, No. 2, 145-152 (1978) · Zbl 0427.76006
[7] Green, A. E.; Naghdi, P. M.: On thermodynamics and the nature of the second law, Proc. roy. Soc. London A 357, 253-270 (1977)
[8] Kannan, K.; Rajagopal, K. R.: A thermomechanical framework for the transition of a viscoelastic liquid to a viscoelastic solid, Math. mech. Solids 9, 37-59 (2004) · Zbl 1043.74003
[9] Kannan, K.; Rao, I. J.; Rajagopal, K. R.: A thermomechanical framework for the Glass transition phenomenon in certain polymers and its application to fiber spinning, J. rheology 46, 977-999 (2002)
[10] Krishnan, J. Murali; Rajagopal, K. R.: Thermodynamic framework for constitutive modeling of asphalt concrete – theory and applications, J. mater. Civ. eng. 16, 155-166 (2004)
[11] Onsager, L.: Reciprocal relations in irreversible thermodynamics, I. phys. Rev. 37, 405-426 (1931) · Zbl 0001.09501
[12] Prigogine, I.: Introduction to thermodynamics or irreversible processes, (1967)
[13] Rajagopal, K.R., 1995. Multiple configurations in continuum mechanics, Report 6, Institute for Computational and Applied Mechanics. University of Pittsburgh.
[14] Rajagopal, K. R.; Srinivasa, A. R.: On the inelastic behavior of solids – part II, energetics of deformation twinning, Int. J. Plasticity 13, 1-35 (1977) · Zbl 0905.73002
[15] Rajagopal, K. R.; Srinivasa, A. R.: Mechanics of the inelastic behavior of materials, part II, Int. J. Plasticity 14, 967-995 (1998) · Zbl 0978.74013
[16] Rajagopal, K. R.; Srinivasa, A. R.: Inelastic behavior of materials: part I – theoretical underpinnings, Int. J. Plasticity 14, 945-967 (1998) · Zbl 0978.74013
[17] Rajagopal, K. R.; Srinivasa, A. R.: Thermomechanical modeling of shape memory alloys, Zeitschrift angewendte Mathematik und physik (ZAMP) 50, 459-496 (1999) · Zbl 0951.74005
[18] Rajagopal, K. R.; Srinivasa, A. R.: A thermodynamic framework for rate-type fluid models, J. non-Newtonian fluid mech. 88, 207-227 (2000) · Zbl 0960.76005
[19] Rajagopal, K. R.; Srinivasa, A. R.: Modeling anisotropic fluids within the framework of bodies with multiple natural configurations, J. non-Newtonian fluid mech. 99, 119-124 (2001) · Zbl 1028.76002
[20] Rao, I. J.; Rajagopal, K. R.: A thermodynamic framework for the study of crystallization in polymers, Zeitschrift angewendte Mathematik und physik (ZAMP) 53, 365-406 (2002) · Zbl 1010.80005
[21] Rivlin, R. S.; Ericksen, J. L.: Stress-deformation relations for isotropic materials, J. rational mech. Anal. 4, 323-425 (1955) · Zbl 0064.42004
[22] Truesdell, C.; Noll, W.: The nonlinear field theories mechanics, (1992) · Zbl 0779.73004
[23] Ziegler, H.: Some extremum principles in irreversible thermodynamics, In progress in solid mechanics 4 (1963)
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