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Statistical mechanics of viscoelasticity

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A unified treatment of viscoelasticity is developed in the framework of non-equilibrium classical statistical mechanics. An exact correspondence between Mori's continued-fractions formalism and rheological circuits is shown.

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References

  1. R. Balescu,Equilibrium and Nonequilibrium Statistical Mechanics (Wiley, New York, 1975), p. 659.

    Google Scholar 

  2. T. H. Barron and M. L. Klein,Proc. Phys. Soc. 85:523 (1964).

    Google Scholar 

  3. F. Bavaud, Ph. Choquard, and J.-R. Fontaine,J. Stat. Phys. 42:621 (1986).

    Google Scholar 

  4. F. Bavaud,J. Stat. Phys. 45:171 (1986).

    Google Scholar 

  5. F. Bavaud,Helv. Phys. Acta 59:1239 (1986).

    Google Scholar 

  6. F. Bavaud, to be published.

  7. B. J. Berne,Statistical Mechanics (Plenum Press, New York, 1977), Part B, Chapter 5.

    Google Scholar 

  8. A. L. Cauchy,Oeuvres Complétes, Série 2 (Gauthier-Villars, Paris, 1890), Vol. 8, pp. 227, 253.

    Google Scholar 

  9. R. M. Christensen,Theory of Viscoelasticity (Academic Press, New York, 1982).

    Google Scholar 

  10. B. D. Coleman and W. Noll,Rev. Mod. Phys. 33:239 (1961).

    Google Scholar 

  11. I. P. Cornfeld, S. V. Fomin, and Y. G. Sinai,Ergodic Theory (Springer-Verlag, New York, 1982), p. 24.

    Google Scholar 

  12. E. A. Desloge,Classical Mechanics (Wiley, New York, 1982), Vol. II, p. 750.

    Google Scholar 

  13. G. P. De Vault and J. A. McLennan,Phys. Rev. 137A:724 (1965).

    Google Scholar 

  14. M. Dupuis,Prog. Theor. Phys. 37:502 (1967).

    Google Scholar 

  15. W. N. Findley, J. S. Lai, and K. Onaran,Creep and Relaxation of Nonlinear Viscoelastic Materials (North-Holland, Amsterdam, 1976).

    Google Scholar 

  16. W. Flügge,Viscoelasticity (Springer-Verlag, Berlin, 1975).

    Google Scholar 

  17. J. Forencio and M. H. Lee,Phys. Rev. A 31:3231 (1985).

    Google Scholar 

  18. R. F. Fox,Phys. Rev. A 27:3216 (1983).

    Google Scholar 

  19. H. S. Green,Proc. Phys. Soc. A 189:103 (1947).

    Google Scholar 

  20. H. S. Green,The Molecular Theory of Fluids (North-Holland, Amsterdam, 1952), p. 181.

    Google Scholar 

  21. M. S. Green,J. Chem. Phys. 22:398 (1954).

    Google Scholar 

  22. P. Grigolini, G. Grosso, G. P. Parravicini, and M. Sparpaglione,Phys. Rev. B 27:7342 (1983).

    Google Scholar 

  23. B. Gross,Mathematical Structure of the Theories of Viscoelasticity (Hermann, Paris, 1953).

    Google Scholar 

  24. S. C. Hunter, inProgress in Solid Mechanics, Volume I, I. N. Sneddon and R. Hill, eds. (North-Holland, Amsterdam, 1964).

    Google Scholar 

  25. R. Kubo,J. Phys. Soc. Japan 12:570 (1957).

    Google Scholar 

  26. L. Landau and E. Lifschitz,Theorie de l`Élasticité (Wiley, New York, 1967), p. 19.

    Google Scholar 

  27. O. E. Lanford, inDynamical Systems, J. Moser, ed. (Springer-Verlag, Berlin, 1975), p. 14.

    Google Scholar 

  28. J. L. Lebowitz,Phys. Fluids 3:64 (1960).

    Google Scholar 

  29. M. H. Lee,Phys. Rev. Lett. 49:1072 (1982).

    Google Scholar 

  30. A. E. H. Love,The Mathematical Theory of Elasticity (Dover, New York, 1944), p. 14.

    Google Scholar 

  31. J. A. McLennan,Phys. Fluids 3:493 (1960).

    Google Scholar 

  32. J. A. McLennan,Prog. Theor. Phys. 30:408 (1963).

    Google Scholar 

  33. E. W. Montroll,Rend. Scuola Intern. Fis. Enrico Fermi, Corso 10 (Zanichelli, Bologna, 1960), p. 242.

    Google Scholar 

  34. H. Mori,Phys. Rev. 112:1829 (1958).

    Google Scholar 

  35. H. Mori,Prog. Theor. Phys. 28:763 (1962).

    Google Scholar 

  36. H. Mori,Prog. Theor. Phys. 34:399 (1965).

    Google Scholar 

  37. F. D. Murnaghan,Ann. J. Math. 49:235 (1937).

    Google Scholar 

  38. O. Perron,Die Lehre von den Kettenbrüchen (Chelsea, New York, 1929), p. 320.

    Google Scholar 

  39. M. Reed and B. Simon,Methods of Modern Mathematical Physics (Academic Press, New York, 1975), Vol. II, p. 13.

    Google Scholar 

  40. P. Résibois and M. De Leener,Classical Kinetic Theory of Fluids (Wiley, New York, 1977), p. 287.

    Google Scholar 

  41. A. Siegert and E. Meeron,J. Math. Phys. 7:741 (1966).

    Google Scholar 

  42. T. J. Stieltjes,Oeuvres Complétes (P. Noordhoff, Groningen, 1918), Vol. 2, p. 402.

    Google Scholar 

  43. D. R. Squire, A. C. Holt, and W. G. Hoover,Physica 42:388 (1969).

    Google Scholar 

  44. S. Toxvaerd,J. Chem. Phys. 82:5658 (1985).

    Google Scholar 

  45. H. S. Wall,Analytic Theory of Continued Fractions (New York, 1967), p. 120.

  46. D. C. Wallace,Thermodynamics of Crystals (Wiley, New York, 1974), p. 20.

    Google Scholar 

  47. J. H. Weiner,Statistical Mechanics of Elasticity (Wiley, New York, 1983), p. 30.

    Google Scholar 

  48. D. N. Zubarev,Nonequilibrium Statistical Mechanics (Plenum Press, New York, 1974), p. 142.

    Google Scholar 

  49. R. Zwanzig,Annu. Rev. Phys. Chem. 16:67 (1965).

    Google Scholar 

  50. R. Zwanzig and R. D. Mountain,J. Chem. Phys. 43:4464 (1966).

    Google Scholar 

  51. H. C. Andersen,J. Chem. Phys. 72:2384 (1980).

    Google Scholar 

  52. M. Parrinello and A. Rahman,J. Appl. Phys. 52:7182 (1981).

    Google Scholar 

  53. J. R. Ray and A. Rahman,J. Chem. Phys. 80:4423 (1984).

    Google Scholar 

  54. W. G. Hoover, D. J. Evans, R. B. Hickmann, A. J. Ladd, W. T. Ashurst, and B. Moran,Phys. Rev. A 22:1690 (1980).

    Google Scholar 

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Bavaud, F. Statistical mechanics of viscoelasticity. J Stat Phys 46, 753–775 (1987). https://doi.org/10.1007/BF01013384

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