Irreversible processes and physical interpretation of rational thermodynamics

Journal of Non-Equilibrium Thermodynamics

Volumn 4, Issue 4, 1979, Pages 229-258

  Bataille, J ^a   Kestin, J ^b  

^a LABORATOIRE DE MÉCANIQUE DES FLUIDES ET D ACOUSTIQUE   (France)

^b BROWN UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

THERMODYNAMICS;

EID: 0018298087     PISSN: 03400204     EISSN: 14374358     Source Type: Journal    
DOI: 10.1515/jnet.1979.4.4.229     Document Type: Article

References (89)

1. Coleman, B. D., Noll, W., The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rat. Mech. Anal., 13 (1963), 167—178.
2. Coleman, B. D., Mizel, V. J., Existence of caloric equations of state in thermodynamics, J. Chem. Phys., 40 (1964), 1116–1125.
3. Coleman, B. D., Thermodynamics of materials with memory, Arch. Rat. Mech. Anal., 17 (1964), 1–46.
4. Coleman, B. D., Mizel, V. J., A general theory of dissipation in materials, Arch. Rat. Mech. Anal., 27 (1968), 255–274.
5. Gurtin, M. E., On the thermodynamics of materials with memory, Arch. Rat. Mech. Anal., 28(1968), 40–50.
6. Truesdell, C., Rational thermodynamics, Mac Graw-Hill, New-York, 1969.
7. Day, W. A., The thermodynamics of simple materials with fading memory, Springer, Berlin 1972.
8. Eringen, A. C., Continuum Physics, Vol. II, Academic Press, New-York, 1975.
9. Nemat-Nasser, S., On equilibrium thermodynamics of viscoelasticity and viscoplasticity, in Foundations of Continuum Thermodynamics, ed. J. J. Delgado Domingos, Mac Millan, London, 1974.
10. Meixner, J., Reik, H. G., Thermodynamik der irreversiblen Prozesse, in Handbuch der Physik, vol. III/2, Springer, Berlin 1959.
11. Prigogine, I., Introduction to thermodynamics of irreversible processes, John Wiley, New-York, 1967.
12. De Groot, S. R., Mazur, P., Non equilibrium thermodynamics, North Holland Publishing Company, Amsterdam, 1969.
13. Germain, P., Thermodynamique des milieux continus, Entropie, 55 (1974), 7—14.
14. Bekarevitch, I. L., Khalatnikov, I. M., Sov. Phys. JEPT, 13 (1961), 643.
15. Kestin, J., A course in Thermodynamics, Vol. II, Blaisdell, Waltham, 1968.
16. Kestin, J., On the Application of the Principles of Thermodynamics to Strained Solid Materials, Proc. I.U.T.A.M. Symp., Vienna, 1966.
17. Kestin, J., Rice, J. R., Paradoxes in the Application of Thermodynamics to Strained Solids (in: A Critical Review of Thermodynamics), Stuart, E. B., Gal-Or, B., Brainard, A. J., eds., Mono Book Corp., New-York, 1970, p. 275.
18. Rice, J. R., On the Structure of Stress Strain Relations for Time-Dependent Plastic Deformation in Metals, J. Appl. Mech., 37 (1970), 728—734.
19. Mandel, J., Plasticité classique et viscoplasticité, Courses and Lectures, No. 97, Udine (1971), Springer, Heidelberg, 1973.
20. Mandel, J., Equations constitutives et directeurs dans les milieux plastiques et viscoplastiques, Int. J. Sol. Struct., 9 (1973), 725–540.
21. Ponter, A. R. S., Bataille, J., Kestin, J., A thermodynamic model for the time dependent plastic deformation of solids, To appear in J. de Mécanique (1979).
22. Müller I., On the Entropy Inequality, Arch. Rat. Mech. Anal., 26 (1967), 118—141.
23. Edelen, D. G. B., Non local field theories, in continuum physics, Vol. IV, A. C. Eringen, Ed., Academic Press, New-York, 1967.
24. Prigogine, I., Le domaine de validité de la thermodynamique des phénomènes irréversibles, Physica, 15, (1949), 272—284.
25. Meixner, J., The Entropy Problem in Thermodynamics of Processes, Rheol Acta, 12, (1973), 381–383.
26. Bridgmann, P. W., The nature of thermodynamics, Harvard University Press, Harvard, 1941.
27. Mandel’Shtam, N. N., Leontovich, M. A., paper dated 1937, quoted by Landau and Lifchitz in Mécanique des Fluides, Mir, Moscow 1971. See also engl. transl. by J. B. Sykes and W. H. Feid, Pergamon Press, New-York, 1959.
28. Meixner, J., Thermodynamik und Relaxationserscheinungen, Z. für Naturforschung, 4a (1949), 594–600.
29. Meixner, J., Die thermodynamische Theorie der Relaxationserscheinungen und ihr Zusammenhang mit der Nachwirkungstheorie, Kolloid Z., 134 (1953), 3—20.
30. Biot, M. A., Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena, J. Appl. Phys., 25 (1954), 1385—1391.
31. Biot, M. A., Variational principles in irreversible thermodynamics with application to viscoelasticity, Phys. Rev., 97 (1955), 1463.
32. Meixner, J., On the thermodynamic theory of second viscosity, Proc. Roy. Soc. Lond., A 226 (1954), 51–56.
33. Meixner, J., Thermo dynamische Theorie der elastischen Relaxation., Z. für Naturforschung, 9a (1954), 654–663.
34. Meixner, J., Thermodynamische Erweiterung der Nachwirkungstheorie, Z. für Physik 139 (1954), 40–43.
35. Prigogine, I., Mazur, P., Physica, 19 (1953), 241.
36. Eringen, A. C., Irreversible thermodynamics and elastic media, Phys. Rev. 117 (1960), 1174–1183.
37. Schapery, R. A., Thermo-mechanical phenomena in viscoelastic media, J. Appl. Phys., 35 (1964), 1451.
38. Coleman, B. D., Gurtin, M. E., Thermodynamics with internal state variables, J. Chem. Phys., 47 (1967), 597–613.
39. Valanis, K. C., Unified theory of thermomechanical behaviour of viscoelastic materials, in Mechanical behaviour of materials under dynamic loads, Londholm, N. N., Ed., Springer, Berlin, 1968.
40. Meixner, J., Thermodynamik der Vorgänge in einfachen fluiden Medien und die Charakterisierung der Thermodynamik irreversibler Prozesse, Z. für Physik, 219 (1969), 79—104.
41. Meixner, J., Thermodynamics of Processes, Lectures at Lehigh University, Lehigh University Press, Lehigh, 1969—70.
42. Rice, J. R., Inelastic constitutive relations for solids: an internal variable theory and its application to metal plasticity, J. Mech. Phys. Solids, 19 (1971), 433—455.
43. Valanis, K. C., Irreversible thermodynamics of continuous media. International Center for Mechanical Sciences, Course No. 77, Udine (1971), Springer, Berlin, 1972.
44. Perzyna, P., Thermodynamics of rheological materials with internal changes, J. de Mécanique, 10(1971), 391–408.
45. Lubliner, J., On the thermodynamic foundations of non linear solid mechanics, Int. J. Non Linear Mechanics, 7 (1972), 237—254.
46. Lubliner, J., On the structure of the rate equations of materials with internal variables, Acta Mechanica, 17(1973), 109—119.
47. Sidoroff, F., Variables internes en viscoélasticité, I—III, J. de Mécanique, 14 (1975), 545-566;
48. Sidoroff, F., Variables internes en viscoélasticité, I—III, J. de Mécanique, 14(1975), 571-595;
49. Sidoroff, F., Variables internes en viscoélasticité, I—III, J. de Mécanique, 14(1976), 85–118.
50. Rivlin, R. S., The thermomechanics of materials with fading memory, in theoretical Rheology, ed. J. F. Hutton et al., 1975.
51. Meixner, J., Entropy and entropy production, in Foundations of Continuum thermodynamics, Ed., J. J. Delgado Domingos, Mac Millan, London, 1974.
52. Mandel, J., Thermodynamics and Plasticity, in Foundations of continuum thermodynamics, J. J. Delgado Domingos, Ed., Mac Millan, London, 1974.
53. Halphen, B., Nguyen, Qu. S., Sur les matériaux standards generalises, J. de Mécanique, 14 (1975), 39–63.
54. Woods, L. D., The thermodynamics of fluid systems, Oxford University Press, Oxford, 1974.
55. Kestin, J., Bataille, J., Irreversible Thermodynamics of Continua and Internal Variables, in Continuum Models of Discrete Systems, Study No. 12, J. W. Provan, Ed., University of Waterloo Press, Waterloo 1978.
56. Bataille, J., Kestin, J., L’interprétation physique de la thermodynamique rationnelle, J. de Mécanique 14(1975), 365–384.
57. Kestin, J., A course in thermodynamics, Vol. II, Blaisdell, 1968, reprint Hemisphere and Mc. Graw Hill, New York, 1978.
58. Caratheodory, C., Investigation into the foundations of thermodynamics, Math. Annalen 67(1909), 355–386.
59. Edelen, D. G. B., A thermodynamics with internal degrees of freedom and non conservative forces, Int. J. Eng. Sci., 14(1976), 1013—1032.
60. Meixner, J., Tip has many faces, Proc. I. U. T. A. M. Symposium, Vienna (1966), H. Parkus, Ed., Springer, Berlin, 1967.
61. Gurtin, M. E., Vargas, A. S., On the classical theory of reacting fluid mixtures, Arch. Rat. Mech. Anal.,43(1971),198.
62. Lance, M., Gence, J. N., Bataille, J., Forme du flux d’entropie, Int. J. Heat and Mass Transfer, 20(1977), 725–729.
63. Callen, H. B., Thermodynamics, Wiley, New-York, 1960.
64. Eringen, A. C., Continuum Physics, Vol. I, Academic Press, New-York, 1975.
65. Edelen, D. G. B., On the existence of symmetry relations and dissipation potentials, Arch. Rat. Mech. Anal. 51 (1973), 218–227.
66. Edelen, D. G. B., General solution of the dissipation inequality, J. Non Eq. Thermodyn., 2(1977), 205–210.
67. Muschik, W., Versuch einer phänomenologischen Begründung erweiterter Casimir-Onsagerscher Reziprozitätsbeziehungen, Z. für Physik, 203 (1967), 273—288.
68. Germain, P., Cours de Mécanique des Milieux Continus, Tome I, Masson, Paris, 1973.
69. Bataille, J., Edelen, D. G. B., Kestin, J., On the structuring of thermodynamic fluxes: a direct implementation of the dissipation inequality, To appear in Int. J. Eng. Sci., 1979.
70. Gibert, R., Sur une généralisation des relations d’Onsager, C. R. Acad. Sci. Paris, 236 (1953), 2165–2167
71. Dodé, M., Sur la validité générale des relations réciproques de Gibert-Onsager, C. R. Acad. Sci. Paris, 243 (1956), 888–891.
72. Péneloux, A., Démonstration des relations réciproques de Gibert pour les systemes chimiques, C. R. Acad. Sci. Paris, 244, (1957) 2238—2240.
73. Gyarmati, I., Non Equilibrium Thermodynamics, Springer, Berlin, 1970.
74. Van Rysselberghe, P., General Reciprocity Relation between the rates and affinities of simultaneous chemical reactions, J. Chem. Phys. 36, (1962), 1329—1330.
75. Muschik, W., A Phenomenological Foundation of Non-linear Onsager-Casimir Reciprocity Relations, J. Non-Equilib. Thermodyn. 2 (1977), 109—124.
76. Nemat-Nasser, S., On Non-Equilibrium Thermodynamics of Continua: Addendum, in Mechanics Today, Vol. 4, Pergamon Press, New-York, in press, 1979.
77. Edelen, D. G. B., Properties of a very elementary class of fluids with non dissipative viscous stresses, To appear, 1977.
78. Moreau, J. J., Sur les lois de frottement de viscosité et de plasticité, C. R. Acad. Sci. Paris, 271 (1970), 608–611.
79. Ziegler, H., A possible generalization of Onsager’s theory, Proc. I. U. T. A. M. Symp. Vienna (1966), H. Parkus, Ed., Springer, Berlin, 1967.
80. Ziegler, H., Thermomechanics, Quart. Appl. Math., 30 (1972), 91 — 107.
81. Lam, L., Dissipation functions and conservation laws of molecular liquids and solids, Z. Physik, B 27 (1977), 101–110.
82. Li, J. C. M., J. Phys. Chem. 66 (1962), 1414–1420.
83. Lubliner, J., On fading memory in materials of evolutionary type, Acta Mech., 8(1969), 75–81.
84. Bataille, J., Kestin, J., General forms of the dissipation inequality. J. Non-Equilib. Thermodyn. 1 (1976), 25–31.
85. Meixner, J., Processes in simple thermodynamic materials, Arch. Rat. Mech. Anal., 33 (1969), 33–53.
86. Keller, J. U., Eine Folgerung aus der Fundamentalen Ungleichung der Thermodynamik, Physica, (1970), 451–457.
87. Ferziger, J. H., Kaper, A. G., Mathematical Theory of Transport Processes in Gases, North Holland Publishing Co., Amsterdam, 1972.
88. Chapman, S., Cowling, T. G., The Mathematical theory of Non-Uniform Gases, Cambridge Univ. Press, England, 2nd Ed., 1964.
89. Hirschfelder, J. O., Curtiss, C. F., Bird, R. B., Molecular theory of gases and liquids, John Wiley, New York, 2nd Ed., 1964.