Constitutive behavior modeling and fractional derivatives

Rheology Series

Volumn 8, Issue C, 1999, Pages 429-466

  Friedrich, Chr ^a   Schiessel, H ^a,b   Blumen, A ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0342619501     PISSN: 01693107     EISSN: None     Source Type: Book Series    
DOI: 10.1016/S0169-3107(99)80038-0     Document Type: Article

References (74)

1. In: Richert R., and Blumen A. (Eds). Disorder Effects on Relaxational Processes: Glasses, Polymers, Proteins (1994), Springer, Berlin
2. Blumen A. In: Dorfmüller Th., and Williams G. (Eds). Molecular Dynamics and Relaxation Phenomena in Glasses (1987), Springer, Berlin 1
3. In: Klafter J., Rubin R.J., and Shlesinger M.F. (Eds). Transport and Relaxation in Random Materials (1986), World Scientific, Singapore
4. Ngai K.L., and Wright G.B. Relaxation in Complex Systems (1984), Naval Research Lab., Springfield, VA
5. Williams G., and Watts D.C. Trans. Faraday Soc. 66 (1970) 80
6. Williams G. Adv. Polym. Sci. 33 (1979) 59
7. Kohlrausch F. Pogg Ann. Physik 29 (1863) 337
8. Friedrich J., and Blumen A. Phys. Rev. B 32 (1985) 1434
9. Tobolsky A.V., and Catsiff E. Journal of Polymer Science 19 (1956) 111
10. M. Mours and H.H. Winter, Chapter in this book.
11. Friedrich Chr., and Braun H. Colloid Polym. Sci. 272 (1994) 1536
12. Friedrich Chr. Rheol. Acta 30 (1991) 151
13. Friedrich Chr. In: Casas-Vázquez J., and Jou D. (Eds). Rheological modelling: Thermodynamical and Statistical Approaches. Lecture Notes in Physics No. 381 (1991), Springer, Berlin 321
14. Friedrich Chr., and Braun H. Rheol. Acta 31 (1992) 309
15. Friedrich Chr., and Hazanov S. Advances in Structured and Heterogeneous Continua (1994), Allerton Press Inc., New York 173
16. Friedrich Chr., and Heymann L. J. Rheol. 32 (1988) 235
17. Friedrich Chr., Heymann L., and Berger H.-R. Rheol. Acta 28 (1989) 535
18. Friedrich Chr. J. Non-Newt. Fluid Mech. 46 (1993) 307
19. Friedrich Chr. Phil. Mag. Letters 66 (1992) 287
20. Friedrich Chr., Braun H., and Weese J. Polym. Eng. Sci. 35 (1995) 1661
21. Caputo M., and Meinardi F. Riv. Nuovo Cimento (Ser. 2) 1 (1971) 161
22. Meinardi F., and Bonetti E. Progress and Trends in Rheology II. Suppl. Rheol. Acta 26 (1988) 64
23. Meinardi F. Fractional relaxation in anelastic solids. J. All. & Comp. 211/212 (1994) 534
24. In: Abramowitz M., and Stegun I.A. (Eds). Handbook of Mathematical Functions (1972), Dover, New York
25. Tschoegl N.W. The Phenomenological Theory of Linear Viscoelastic Behavior (1989), Springer, Berlin
26. Ward I.M. Mechanical Properties of Solid Polymers (1983), Wiley, Chichester
27. Oldham K.B., and Spanier J. The Fractional Calculus (1974), Academic, New York
28. Miller K.S., and Ross B. An Introduction to the Fractional Calculus and Fractional Differential Equations (1993), Wiley, New York
29. Gemant A. Physics 7 (1936) 311
30. Gemant A. Phil. Mag. 25 (1938) 540
31. Nutting P.G. J. of the Franklin Institute 191 (1921) 679
32. Nutting P.G. Proc. Amer. Soc. Test. Mater. 21 (1921) 1162
33. Kobeko P., Kuvshinskij E., and Gurevitch G. Techn. Phys USSR 4 (1937) 622
34. Alexandrov A.P., and Lazurkin Yu.S. J. Tech. Fiz. 9 (1939) 1250
35. Alexandrov A.P., and Lazurkin Yu.S. J. Tech. Fiz. 9 (1939) 1261
36. LeMehaute A., Picard L., and Fruchter L. Phil. Mag. B 52 (1985) 1071
37. Scott-Blair G.W., and Coppen F.M.V. Amer. J. Psychol. 56 (1943) 234
38. Caffyn J.E., and Scott-Blair G.W. Nature 155 (1945) 171
39. Scott-Blair G.W., Veinoglou B.C., and Caffyn J.E. Proc. Roy. Soc. Ser. A 189 (1947) 69
40. Scott-Blair G.W., and Caffyn J.E. Phil. Mag. 40 (1949) 80
41. Bosworth R.C.L. Nature 157 (1946) 447
42. Slonimsky G.L. Journal of Polymer Science: Part C 16 (1967) 1667
43. Smit W., and de Vries H. Rheol. Acta 9 (1970) 525
44. Glöckle W.G., and Nonnenmacher T.F. Macromolecules 24 (1991) 6426
45. Nonnenmacher T.F. In: Casas-Vázquez J., and Jou D. (Eds). Lecture Notes in Physics No. 381 (1991), Springer, Berlin 309
46. Nonnenmacher T.F., and Glöckle W.G. Phil. Mag. Letters 64 (1991) 89
47. Koeller R.C. J. Appl. Mech. 51 (1984) 299
48. Rabotnov Y.N. Elements of Hereditary Solid Mechanics (1980), Mir Publishers, Moscow
49. Friedrich Chr., and Hazanov S. In: Siginer D.A., and Yanovsky Y.G. (Eds). Advances in Structured and Heterogeneous Continua (1994), Allerton Press, New York
50. Bagley R.L. J. Rheol. 27 (1983) 201
51. Bagley R.L., and Torvik P.j. J. Rheol. 30 (1986) 133
52. Rogers L. J. Rheol. 27 (1983) 351
53. VanArsdale W.E. J. Rheol. 29 (1985) 851
54. Glöckle W.G., and Nonnenmacher T.F. Rheol. Acta 33 (1994) 337
55. Metzler R., Schick W., Kilian H.-G., and Nonnenmacher T.F. J. Chem. Phys. 103 (1995) 7180
56. Schiessel H., and Blumen A. J. Phys. A 26 (1993) 5057
57. Schiessel H., Alemany P., and Blumen A. Progr. Colloid Polym. Sci. 96 (1994) 16
58. Schiessel H., and Blumen A. Macromolecules 28 (1995) 4013
59. Schiessel H., and Blumen A. Fractals 3 (1995) 483
60. Schiessel H., Metzler R., Blumen A., and Nonnenmacher T.F. J. Phys. A 28 (1995) 6567
61. Bauwens J.-C. Colloid Polym. Sci. 270 (1992) 537
62. Heymans N., and Bauwens J.-C. Rheol. Acta 33 (1994) 210
63. Heymans N. Rheol. Acta 35 (1996) 508
64. Giona M., Cerbelli S., and Roman H.E. Physica A 191 (1992) 449
65. Stastna J., Zanzotto L., and Ho K. Rheol. Acta 33 (1994) 344
66. Odenwald M., Eicke H.-F., and Friedrich Chr. Colloid Polym. Sci. 274 (1996) 568
67. Odenwald M. Diploma-Thesis, Freiburg (1993)
68. Friedrich Chr., and Dehno H. Progress and Trends in Rheology IV (1994), Steinkopffverlag, Darmstadt 45
69. Palade L.I., Verney V., and Attane P. Rheol. Acta 35 (1996) 265
70. Hellinckx S. Colloid Polym. Sci. 275 (1997) 116
71. Havlin S., and Bunde A. In: Bunde A., and Havlin S. (Eds). Fractals and Disordered Systems (1991), Springer, Berlin 97
72. Mours M., and Winter H.H. Macromolecules 29 (1996) 7221
73. Friedrich Chr. Acta Polymerica 46 (1995) 385
74. In: Erdélyi A. (Ed). Bateman Manuscript Project. Higher Transcendental Functions Vol. III (1955), Mc.Graw-Hill, New York