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.
References:
| [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 · doi:10.1007/BF00280970 |
| [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 · doi:10.1016/0020-7225(94)00078-X |
| [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 · doi:10.1007/BF00250351 |
| [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 · doi:10.1016/S0749-6419(98)00037-0 |
| [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 · doi:10.1016/S0749-6419(98)00037-0 |
| [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 · doi:10.1007/s000330050028 |
| [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 · doi:10.1016/S0377-0257(99)00023-3 |
| [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 · doi:10.1016/S0377-0257(01)00116-1 |
| [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 · doi:10.1007/s00033-002-8161-8 |
| [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) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
