Fractional Integral Operators and Fox Functions in the Theory of Viscoelasticity

Macromolecules

Volumn 24, Issue 24, 1991, Pages 6426-6434

  Glöckle, Walter G ^a   Nonnenmacher, Theo F ^a  

^a UNIVERSITY OF ULM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

MATHEMATICAL MODELS; RUBBER - VISCOELASTICITY; VISCOELASTICITY - THEORY;

FOX FUNCTION; POLYISOBUTYLENE; VISCOELASTIC MATERIALS; ZENER MODEL;

POLYBUTENES;

EID: 0026260899     PISSN: 00249297     EISSN: 15205835     Source Type: Journal    
DOI: 10.1021/ma00024a009     Document Type: Article

References (27)

1. Maxwell, J. C. Philos. Trans. R. Soc. 1867, 157, 49.
2. Bagley, R. L.; Torvik, P. J. J. Rheol. 1983, 27, 201.
3. Koeller, R. C. J. Appl. Mech. 1984, 51, 299.
4. Friedrich, C. Rheol. Acta 1991, 30, 151.
5. Douglas, J. F. Macromolecules 1989, 22, 1786.
6. Ferry, J. D. Viscoelastic Properties of Polymers; John Wiley & Sons: New York, 1970.
7. Ward, I. M. Mechanical Properties of Solid Polymers; John Wiley & Sons: Chichester, U.K., 1983.
8. Tschoegl, N. W. The Phenomenological Theory of Linear Viscoelastic Behavior; Springer: Berlin, 1989.
9. Oldham, K. B.; Spanier, J. The Fractional Calculus; Academic Press: New York 1974.
10. Schneider, W. R.; Wyss, W. J. Math. Phys. 1989, 30, 134.
11. Nonnenmacher, T. F.; Nonnenmacher, J. D. F. Acta Phys. Hung. 1989, 66, 145.
12. Nonnenmacher, T. F. In Rheological Modelling: Thermodynamical and Statistical Approaches; Casas-Vázquez, J., Jou, D., Eds.; Lecture Notes in Physics Vol. 381; Springer-Verlag: Berlin, 1991, pp 309–320.
13. Schofield, R. K.; Scott Blair, W. G. Proc. R. Soc. 1932, A138, 707.
14. Tobolsky, A. V.; Catsiff, E. J. Polym. Sci. 1956, 19, 111.
15. Nonnenmacher, T. F.; Glöckle, W. G. Philos. Mag. Lett. 1991, 64, 89.
16. Cole, K. S.; Cole, R. H. J. Chem. Phys. 1941, 9, 341.
17. Ferry, J. D.; Grandine, L. D., Jr.; Fitzgerald, E. R. J. Appl. Phys. 1953, 24, 911.
18. Nonnenmacher, T. F. J. Phys. A: Math. Gen. 1990, 23, L697.
19. Glöckle, W. G.; Nonnenmacher, T. F. Proceedings of the 3rd International Conference Locarno: Stochastic Processes, Physics and Geometry, to be published.
20. Sann, M. Mechanische Spektroskopie an gefüllten Elastomeren. Diploma thesis, University of Ulm, Ulm, Germany, 1990.
21. Nicolai, T.; Brown, W.; Hvidt, S.; Heller, K. Macromolecules 1990, 23, 5088.
22. Pezron, E.; Ricard, A.; Leibler, L. J. Polym. Sci. 1990, 28, 2445.
23. van der Werff, J. C.; de Kruif, C. G.; Blom, C.; Mellema, J. Phys. Rev. A 1989, 39, 795.
24. Fox, C. Trans. Am. Math. Soc. 1961, 98, 395.
25. Braaksma, B. L. J. Compos. Math. 1964, 15, 239.
26. Mathai, A. M.; Saxena, R. K. The H-function with Applications in Statistics and Other Disciplines; Wiley Eastern Limited: New Delhi, India, 1978.
27. Erdélyi, A., Ed. Bateman Manuscript Project, Higher Transcendental Functions; McGraw-Hill Book Co.: New York, 1955; Vol. III.