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Constitutive Laws and Microstructure pp 3–25Cite as

Thermodynamical Constitutive Laws - Outlines -

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Summary

Material theories can be divided into two classes, the probabilistic and the deterministic or phenomenological theories. The probabilistic theories can be decomposed into stochastic, statistical and transporttheoretical branches which are shortly discussed. The phenomenological theories can be divided into two categories, those of discrete systems and those using continuum theoretical concepts which are discussed in more detail.

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References

  1. Muschik, W.: Formulations of the Second Law, Symposium “Statistical Thermodynamics and Semiconductors” Gregynog, Sept. 14-17, 1987, J. Phys. Chem. Solids, to be published.

    Google Scholar 

  2. Axelrad, D.R.: Foundations of the Probabilistic Mechanics of Discrete Media. Oxford: Pergamon Press 1984.

    MATH  Google Scholar 

  3. Fick, E.; Sauermann, G.: Quantenstatistik Dynamischer Systeme, Bd. I. Thun: Harri Deutsch 1983.

    Google Scholar 

  4. Cercignani, C.: Theory and Application of the Boltzmann Equation. New York: Elsevier 1975

    MATH  Google Scholar 

  5. Axelrad, D.R.: Micromechanics of Solids. Amsterdam: Elsevier 1978.

    Google Scholar 

  6. See [2] sec. 3.7 and hints therein.

    Google Scholar 

  7. Fick, E.; Schwegler, H.: Z. Physik 200 (1967) 165.

    Article  MATH  ADS  Google Scholar 

  8. Jaynes, E.T.: Phys. Rev. 106 (1957) 620, 108 (1957) 171.

    Article  ADS  MathSciNet  Google Scholar 

  9. Robertson, B.: Phys. Rev. 144 (1966) 151.

    Article  ADS  MathSciNet  Google Scholar 

  10. Muschik, W.; Fang, J.: Statistical Foundation of Nonequili-brium Contact Quantities Bridging Phenomenological and Statistical Nonequilibrium Thermodynamics, to be published.

    Google Scholar 

  11. Kubo, R.; Toda, M.; Hashitsume, N.: Statistical Physics II. Berlin: Springer 1978, Chap. 4.

    Google Scholar 

  12. Grabert, H.: Projection Operator Techniques in Nonequilibrium Statistical Mechanics, Springer Tracts in Modern Physics 95. Berlin: Springer 1982

    Google Scholar 

  13. Risken, H.: The Fokker-Planck Equation. Berlin: Springer 1984

    MATH  Google Scholar 

  14. Ferziger, J.H.; Kaper, H.G.: Mathematical Theory of Transport Processes in Gases. Amsterdam: North-Holland 1972

    Google Scholar 

  15. Schottky, W.: Thermodynamik, l.Teil §1. Berlin: Springer 1929.

    Google Scholar 

  16. Meixner, J.: Rheol. Acta 7 (1968) 8.

    Article  Google Scholar 

  17. Truesdell, C.; Toupin, R.: The Classical Field Theories; in Handbook of Physics, Vol. III/l. Berlin: Springer 1960, Sect. G.

    Google Scholar 

  18. Truesdell, C.; Noll, W.: The Non-linear Field Theories of Mechanics; in Handbook of Physics, Vol. III/3. Berlin: Springer 1965

    Google Scholar 

  19. Muschik, W.; Brunk, G.: ZAMM 57 (1977) T108.

    MathSciNet  Google Scholar 

  20. Muschik, W.: ZAMM 62 (1982) T143.

    MathSciNet  Google Scholar 

  21. Leigh, D.C.: Nonlinear Continuum Mechanics. New York: McGraw-Hill 1968, Lect. 9

    Google Scholar 

  22. see [18], sec. 29

    Google Scholar 

  23. see [18], sec. 31

    Google Scholar 

  24. Müller, I.: Thermodynamics, Chap.4. Boston: Pitman 1985.

    MATH  Google Scholar 

  25. Kestin, J.: A Course in Thermodynamics, Vol.I, Chap.3. New York: McGraw Hill 1979.

    Google Scholar 

  26. Muschik, W.: ZAMM 61 (1981) T213

    Google Scholar 

  27. Muschik, W.: J. Appl. Sci. 4 (1986) 189

    Google Scholar 

  28. Haase, R.: Thermodynamik der irreversiblen Prozesse. Darmstadt: Steinkopf 1963, § 1.24, § 4.12.

    Google Scholar 

  29. Swenson, R.J.: J. Non-Equilib. Thermodyn. 3 (1978) 39

    Article  ADS  Google Scholar 

  30. Muschik, W.: J. Non-Equilib. Thermodyn. 2 (1977) 109

    Article  ADS  Google Scholar 

  31. Muschik, W.; Trostel, R.: ZAMM 63 (1983) T190

    Google Scholar 

  32. Truesdell, C.: Rational Thermodynamics. New York: McGraw-Hill, Lect. 7.

    Google Scholar 

  33. Hutter, K.: Acta Mechanica 27 (1977) 1

    Article  ADS  MathSciNet  Google Scholar 

  34. see [32], Lect.5 and Lect.6.

    Google Scholar 

  35. see [18], Sect.79

    Google Scholar 

  36. Noll, W.: Arch. Rat. Mech. Anal. 48 (1972) 1

    Article  MATH  MathSciNet  Google Scholar 

  37. Coleman, B.D.; Owen, D.R.: Arch. Rat. Mech. Anal. 54 (1974) 1

    Article  MATH  MathSciNet  Google Scholar 

  38. Müller, I.: Thermodynamik. Düsseldorf: Bertelsmann 1973, Kap. III.5

    MATH  Google Scholar 

  39. Liu, I.S.; Müller, I.: Arch. Rat. Mech. Anal. 83 (1983) 285

    Article  MATH  Google Scholar 

  40. Green, A.E.; Naghdi, P.M.: Arch. Rat. Mech. Anal. 48 (1972) 352

    Article  MATH  MathSciNet  Google Scholar 

  41. Eringen, A.C.: Crystal Lattice Defects 7 (1977) 109

    Google Scholar 

  42. Muschik, W.: in Lecture Notes in Physics 199. Berlin: Springer 1984, p. 387

    Google Scholar 

  43. Coleman, B.D.; Noll, W.: Arch. Rat. Mech. Anal. 13 (1963) 167

    Article  MATH  MathSciNet  Google Scholar 

  44. Coleman, B.D.: Arch. Rat. Mech. Anal. 17 (1964) 1

    Google Scholar 

  45. see [38j, Kap. IV, 2.a

    Google Scholar 

  46. Liu, I.S.: Arch. Rat. Mech. Anal. 46 (1972) 131

    MATH  Google Scholar 

  47. Muschik, W.: in Chien Wei-zang (ed): Proc. Intern. Conf. Nonlinear Mech.(ICNM) Shanghai 1985, p. 155

    Google Scholar 

  48. Müller, I.: Arch. Rat. Mech. Anal. 41 (1971) 319

    Article  MATH  Google Scholar 

  49. see [38], Kap.VI.2

    Google Scholar 

  50. Müller, I.: in Lecture Notes in Physics 199. Berlin: Springer 1984, p. 32

    Google Scholar 

  51. Meixner, J.: Z. Physik 219 (1969) 79

    Article  ADS  Google Scholar 

  52. Day, W.A.: The Thermodynamics of Simple Material with Fading Memory, Springer Tracts in Natural Philosophie, Vol. 22. Berlin: Springer 1972, sec.3.4

    Book  Google Scholar 

  53. Keller, J.U.: Physica 53 (1971) 602

    Article  ADS  Google Scholar 

  54. Bataille, J.; Kestin J.: J. Mécanique 14 (1975) 365

    MATH  ADS  MathSciNet  Google Scholar 

  55. Gurtin, M.E.; Williams, W.: Arch. Rat. Mech. Anal. 26 (1967) 83

    Article  MATH  MathSciNet  Google Scholar 

  56. Muschik, W.: in Reif, F.: Statistische Physik und Theorie der Wärme. Berlin: de Gruyter 1985, Abschn. 15.19

    Google Scholar 

  57. Muschik, W.: in Spencer, A. J. M. (ed.): Continuum Models of Discrete Systems. Rotterdam: Balkema 1987, p.39

    Google Scholar 

  58. Muschik, W.; Brunk, G.: Int. J. Engng. Sci. 15 (1977) 377

    Article  MathSciNet  Google Scholar 

  59. Muschik, W.: Arch. Rat. Mech. Anal. 66 (1977) 379

    Article  MathSciNet  Google Scholar 

  60. Muschik, W.: Int. J. Engng. Sci. 18 (1980) 1399

    Article  MATH  MathSciNet  Google Scholar 

  61. Müller, W.H.; Muschik, W.: J. Non-Equilib. Thermodyn. 8 (1983) 29

    Article  ADS  Google Scholar 

  62. Muschik, W.; Riemann, H.: J. Non-Equilib. Thermodyn. 4 (1979) 17

    Article  ADS  Google Scholar 

  63. Muschik, W.: J. Non-Equilib. Thermodyn. 8 (1983) 219

    Article  ADS  Google Scholar 

  64. Muschik, W.: J. Non-Equilib. Thermodyn. 4 (1979) 377

    Article  ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstraße 36, D-1000, Berlin 12, Germany

    W. Muschik

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  1. W. Muschik
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Editor information

Editors and Affiliations

  1. Department of Mechanical Engineering, McGill University, Montreal, Quebec, Canada

    David R. Axelrad

  2. Institut for Theoretical Physics, Technical University of Berlin, Hardenbergstraße 36, D-1000, Berlin 12, Germany

    Wolfgang Muschik

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© 1988 Springer-Verlag, Berlin, Heidelberg

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Muschik, W. (1988). Thermodynamical Constitutive Laws - Outlines -. In: Axelrad, D.R., Muschik, W. (eds) Constitutive Laws and Microstructure. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83303-8_1

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  • DOI: https://doi.org/10.1007/978-3-642-83303-8_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83305-2

  • Online ISBN: 978-3-642-83303-8

  • eBook Packages: Springer Book Archive

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