A nonlinear fractional viscoelastic material model for polymers

Computational Materials Science

Volumn 50, Issue 10, 2011, Pages 2938-2949

  Müller, Sebastian ^a   Kästner, Markus ^a   Brummund, Jörg ^a   Ulbricht, Volker ^a  

^a INSTITUTE OF SOLID MECHANICS   (Germany)

Author keywords

Fractional calculus; Nonlinear viscoelasticity; Polymer

Indexed keywords

EXPERIMENTAL OBSERVATION; EXPERIMENTAL TEST; FRACTIONAL CALCULUS; INELASTIC MATERIALS; LOADING AND UNLOADING; MATERIAL PARAMETER; MECHANICAL BEHAVIOR; MULTIAXIAL; NON-LINEAR VISCOELASTICITY; SMALL STRAINS; TENSILE TESTS; TEST SCHEME; VISCO-ELASTIC MATERIAL;

CONSTITUTIVE EQUATIONS; MATERIALS; POLYMERS; TENSILE TESTING; UNLOADING; VISCOELASTICITY;

FINITE ELEMENT METHOD;

EID: 79959492925     PISSN: 09270256     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.commatsci.2011.05.011     Document Type: Article

References (61)

1. H. Altenbach, and V. Eremeyev Acta Mechanica 204 3 2009 137 154
2. A. Amin, A. Lion, S. Sekita, and Y. Okui International Journal of Plasticity 22 9 2006 1610 1657
3. E.M. Arruda, and M.C. Boyce International Journal of Plasticity 9 6 1993 697 720
4. E.M. Arruda, and M.C. Boyce Journal of the Mechanics and Physics of Solids 41 2 1993 389 412
5. E.M. Arruda, M.C. Boyce, and R. Jayachandran Mechanics of Materials 19 2-3 1995 193 212
6. R.L. Bagley, and P.J. Torvik Journal of Rheology 27 3 1983 201 210
7. R.L. Bagley, and P.J. Torvik Journal of Rheology 30 1 1986 133 155
8. M. Caputo, and F. Mainardi La Rivista del Nuovo Cimento (1971-1977) 1 2 1971 161 198
9. S. Coiai, E. Passaglia, A. Hermann, S. Augier, D. Pratelli, and R.C. Streller Polymer Composites 31 4 2010 744 754
10. K. Diethelm, N. Ford, A. Freed, and Y. Luchko Computer Methods in Applied Mechanics and Engineering 194 6-8 2005 743 773
11. K. Diethelm, N.J. Ford, and A.D. Freed Nonlinear Dynamics 29 1 2002 3 22
12. A. Drozdov International Journal of Solids and Structures 46 18-19 2009 3336 3345
13. A. Drozdov, and J. Christiansen Computational Materials Science 39 2 2007 465 480
14. A. Drozdov, and J. Christiansen Polymer 48 10 2007 3003 3012
15. A. Drozdov, A.-L. Hog Lejre, and J.d. Christiansen Composites Science and Technology 69 15-16 2009 2596 2603
16. A.D. Drozdov International Journal of Solids and Structures 35 18 1998 2315 2347
17. A.D. Drozdov, and J.D. Christiansen Polymer Engineering & Science 43 4 2003 946 959
18. I. Emri, and N.W. Tschoegl Rheologica Acta 32 3 1993 311 322
19. M. Enelund, and P. Olsson International Journal of Solids and Structures 36 7 1999 939 970
20. C. Friedrich Rheologica Acta 30 2 1991 151 158
21. R. Gorenflo, Fractals and Fractional Calculus in Continuum Mechanics, Springer Verlag, Wien and New York, 1997, pp. 277-290 (Chapter Fractional Calculus: Some Numerical Methods).
22. R. Gorenflo, F. Mainardi, Fractional calculus: Integral and differential equations of fractional order, 1997.
23. R. Gorenflo, F. Mainardi, Essentials of fractional calculus, 2000.
24. R. Gorenflo, F. Mainardi, Fractional calculus: Integral and differential equations of fractional order, 2008. ArXiv e-prints: 0805.3823.
25. S. Govindjee, and J.C. Simo International Journal of Solids and Structures 29 14-15 1992 1737 1751
26. P. Haupt Acta Mechanica 100 3 1993 129 154
27. P. Haupt second ed. 2002 Springer Verlag Berlin Heidelberg
28. P. Haupt, and A. Lion Continuum Mechanics and Thermodynamics 7 1 1995 73 96
29. P. Haupt, and K. Sedlan Archive of Applied Mechanics 71 2 2001 89 109
30. G. Heinrich, and M. Kaliske Computational and Theoretical Polymer Science 7 3-4 1997 227 241
31. M. Kaliske, and G. Heinrich Rubber Chemistry and Technology 72 4 1999 602 632
32. M. Kaliske, and H. Rothert Computational Mechanics 19 3 1997 228 239
33. M. Kästner, Skalenübergreifende modellierung und simulation des mechanischen verhaltens von textilverstärktem polypropylen unter nutzung der xfem, Dissertation, Technische Universität Dresden, 2009. < http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-27515 >.
34. M. Kästner, G. Haasemann, J. Brummund, and V. Ulbricht Computation of Effective Stiffness Properties for Textile-Reinforced Composites Using X-FEM 2008 Springer pp. 261-279 (Chapter 13)
35. M. Kästner, G. Haasemann, and V. Ulbricht International Journal for Numerical Methods in Engineering 86 4-5 2011 477 498
36. M. Kitagawa, and H. Takagi Journal of Materials Science 25 6 1990 2869 2872
37. R.C. Koeller Journal of Applied Mechanics 51 2 1984 299 307
38. A. Lion Continuum Mechanics and Thermodynamics 8 3 1996 153 169
39. A. Lion Journal of the Mechanics and Physics of Solids 45 11-12 1997 1805 1834
40. A. Lion Continuum Mechanics and Thermodynamics 9 2 1997 83 96
41. A. Lion Acta Mechanica 123 1 1997 1 25
42. Mainardi, F., 1997. Fractals and Fractional Calculus in Continuum Mechanics, CISM Courses and Lecture Notes, vol. 378, Springer Verlag, pp. 291-348 (Chapter Fractional Calculus: Some Basic Problems in Continuum and Statistical Mechanics).
43. F. Mainardi, and R. Gorenflo Journal of Computational and Applied Mathematics 118 1-2 2000 283 299
44. F. Mainardi, and R. Gorenflo Fractional Calculus and Applied Analysis 10 3 2007 269 308
45. C. Miehe, and J. Keck Journal of the Mechanics and Physics of Solids 48 2 2000 323 365
46. K.S. Miller, and B. Ross An Introduction to the Fractional Calculus and Fractional Differential Equations first ed. 1993 John Wiley & Sons (May 19, 1993)
47. M.G. Mittag-Leffler Comptes Rendus de l Academie des Sciences Serie II Paris 137 1903 554 558
48. T.F. Nonnenmacher, and W.G. Glöckle Philosophical Magazine Letters 64 2 1991 89 93
49. R.W. Ogden, and D.G. Roxburgh Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences 455 1988 1999 2861 2877
50. K.B. Oldham, and J. Spanier The Fractional Calculus 1974 Academic Press New York
51. I. Podlubny Fractional Differential Equations 1999 Academic Press San Diego
52. T. Pritz Journal of Sound and Vibration 265 5 2003 935 952
53. S. Reese, and S. Govindjee International Journal of Solids and Structures 35 26-27 1998 3455 3482
54. H. Schiessel, R. Metzler, A. Blumen, and T.F. Nonnenmacher Journal of Physics A: Mathematical and General 28 23 1995 6567 6584
55. A. Schmidt, and L. Gaul Nonlinear Dynamics 29 1 2002 37 55
56. Sedlan, K., 2000. Viskoelastisches materialverhalten von elastomerwerkstoffen: Experimentelle untersuchung und modellbildung. Dissertation, Universität Gesamthochschule Kassel.
57. J. Simo, and T. Hughes Computational Inelasticity (Interdisciplinary Applied Mathematics) 1998 Springer Verlag
58. J.C. Simo Computer Methods in Applied Mechanics and Engineering 60 2 1987 153 173
59. W. Smit, and H. de Vries Rheologica Acta 9 4 1970 525 534
60. N. Tschoegl The Phenomenological Theory of Linear Viscoelastic Behavior-An Introduction 1989 Springer
61. S.w.J. Welch, R.A.L. Rorrer, and R.G. Duren Mechanics of Time-Dependent Materials 3 3 1999 279 303