Thermomechanically consistent formulations of the standard linear solid using fractional derivatives

Archives of Mechanics

Volumn 53, Issue 3, 2001, Pages 253-273

  Lion, A ^a  

^a UNIVERSITY OF KASSEL   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0012671990     PISSN: 03732029     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. R. L. BAGLEY, P. J. TORVIK, Fractional calculus- a different approach to the analysis of viscoelastically damped structures, J. AIAA, 21, 741-748, 1983.
2. R. L. BAGLEY, P. J. TORVIK, On the fractional calculus of viscoelastic behaviour, J. of Rheology, 30, 133-155, 1986.
3. M. CAPUTO, F. MAINARDI, Linear models in anelastic solids, Riv. Il Nuovo Cimento (Serie. II), 1, 161-198, 1971.
4. C. FRIEDRICH, Relaxation functions of Theological constitutive equations with fractional derivatives: thermodynamical constraints, Rheological Modelling: Thermodynamical and Statistical Approaches, 321-330, Springer Verlag, Berlin, Heidelberg 1991.
5. B. GROSS, Mathematical structure of the theories of linear viscoelasticity, Hermann Ltd., Paris 1968.
6. S. HARTMANN, A. LION, P. HAUPT, Zur Modellierung von Kriecheigenschaften von Beton, Zeitschr. Angew. Math. Mech., 78, 457-458, 1997.
7. P. HAUPT, A. LION, E. BACKHAUS, On the dynamic behaviour of polymers during finite strains: constitutive modelling and identification of parameters, Int. J. Solids Struct., 37, 3633-3646, 2000.
8. P. HAUPT, Continuum mechanics and theory of materials, Springer Ltd., 2000.
9. N. HEYMANS, J. C. BAUWENS, Fractal Theological models and fractional differential equations for viscoelastic behaviour, Rheologica Acta, 33, 210-219, 1994.
10. R. C. KOELLER, Applications of fractional calculus to the theory of viscoelasticity, J. of Applied Mechanics, 51, 299-307, 1984.
11. A. LION, On the thermodynamics of fractional damping elements, Continuum Mech. Thermodyn., 9, 83-96, 1997.
12. A. LION, Thixotropic behaviour of rubber under dynamic loading histories: experiments and theory, J. Mech. Phys. Solids., 46, 895-930, 1998.
13. A. LION, Strain-dependent dynamic properties of filled rubber: a nonlinear viscoelastic approach based on structural variables, Rubber Chem. Technol., 72, 410-429, 1999.
14. A. LION, Thermomechanik von Elastomeren: Experimente und Materialtheorie, Habilitation Thesis, University of Kassel, Department of Mechanical Engineering, Institute of Mechanics, Germany 2000.
15. F. MAINARDI, E. BONETTI, The application of real order derivatives in linear viscoelasticity, Rheologica Acta, 26, 64-67, 1988.
16. R. METZELER, W. SCHICK, H. G. KILIAN, T. F. NONNEMACHER, Relaxation in filled polymers: a fractional calculus approach, J. Chem. Phys., 103, 7180-7186, 1995.
17. T. F. NONNENMACHER, Fractional relaxation equations for viscoelasticity and related phenomena, Rheological Modelling: Thermodynamical and Statistical Approaches, 309-320, Springer Verlag, 1991.
18. K. B. OLDHAM, J. SPANIER, The fractional calculus: theory and applications of differentiation and integration to arbitrary order, Academic Press London 1974.
19. A. SCHMIDT, S. OEXL, L. GAUL, Modellierung des viskoelastischen Werkstoffverhaltens von Kunststoffen mit fraktionalen Zeitableitungen, Proceedings of the 18th CAD-FEM Users Meeting, International Congress on FEM Technology, 2000.
20. N. W. TSCHOEGL, The phenomenological theory of linear viscoelastic behaviour, Springer Ltd., 1989.
21. J. D. FERRY, Viscoelastic properties of polymers, John Wiley and Sons.