Effective properties of a linear viscoelastic composite

International Applied Mechanics

Volumn 45, Issue 10, 2009, Pages 1084-1091

  Selivanov, M F ^a  

^a S P TIMOSHENKO INSTITUTE OF MECHANICS   (Ukraine)

Author keywords

Relaxation function; Viscoelastic composite; Viscoelastic moduli

Indexed keywords

APPROXIMATION ALGORITHMS; COMPOSITE MATERIALS; LAPLACE TRANSFORMS; VISCOELASTICITY;

COMPOSITE COMPONENTS; FRACTIONAL-RATIONAL APPROXIMATIONS; LINEAR VISCOELASTIC; MITTAG-LEFFLER FUNCTIONS; REINFORCED COMPOSITES; RELAXATION FUNCTIONS; VISCOELASTIC COMPOSITES; VISCOELASTIC MODULI;

RATIONAL FUNCTIONS;

EID: 77950843201     PISSN: 10637095     EISSN: 15738582     Source Type: Journal    
DOI: 10.1007/s10778-010-0249-9     Document Type: Article

References (26)

1. V. T. Glushko, N. N. Dolinina, and M. I. Rozovskii, Stability of Mine Workings (Mathematical Formulation) [in Russian], Naukova Dumka, Kyiv (1973).
2. M. A. Koltunov, Creep and Relaxation [in Russian], Vyshchaya Shkola, Moscow (1976).
3. N. K. Kucher, M. P. Zemtsov, and M. N. Zarazovskii, "Deformation of laminated epoxy composites reinforced with high-strength fibers, " Strength of Materials, 38, No. 1, 27-38 (2006).
4. B. Ya. Pobedrya, Mechanics of Composite Materials [in Russian], Izd. Mosk. Univ., Moscow (1984).
5. V. N. Poturaev, V I. Dyrda, and I. I. Krush, Applied Mechanics of Rubber [in Russian], Naukova Dumka, Kyiv (1980).
6. Yu. N. Rabotnov, Elements of Hereditary Solid Mechanics [in Russian], Nauka, Moscow (1977).
7. V. Ya. Skorobogat'ko, Theory of Branching Continued Fractions and Its Application in Computational Mathematics [in Russian], Nauka, Moscow (1983).
8. L. P. Khoroshun, B. P. Maslov, E. N. Shikula, and L. V. Nazarenko, Statistical Mechanics and Effective Properties of Materials, Vol. 3 of the 12-volume series Mechanics of Composite Materials [in Russian], Naukova Dumka, Kyiv (1993).
9. M. Alcoutlabi and J. J. Martinez-Vega, "Modeling of the viscoelastic behavior of amorphous polymers by the differential and integration fractional method: the relaxation spectrum H (τ), Polymer, 44, 7199-7208 (2003).
10. T. M. Atanackovitc, "On a distributed derivative model of a viscoelastic body, C. R. Mecanique, 331, 687-692 (2003).
11. R. L. Bagleyand P. J. Torvik, "On the fractional calculus model of viscoelastic behavior, " J. Rheol., 30, 133-155 (1986).
12. L. C. Brinson and W. S. Lin, "Comparison of micromechanical methods for effective properties of multiphase viscoelastic composites", Comp. Struct., 41, 353-367 (1998).
13. F. Cortes and M. J. Elejabarrieta, "Modelling viscoelastic materials whose storage modulus is constant with frequency", Int. J. Solids Struct., 43, 7721-7726 (2006). (Pubitemid 44740292)
14. I. Emri, B. C. Von Bernstorf, R. Cvelbar, and A. Nikonov, "Re-examination of the approximate methods between frequency-and time-dependent material functions", J. Non-Newtonian FluidMech., 129, 74-85 (2005). (Pubitemid 41372537)
15. G. V. Gavrilov, "Study into the kinetics of a crack with a nonsmall fracture process zone in an aging viscoelastic plate", Int. Appl. Mech., 43, No. 8, 903-911 (2007).
16. L. V. Gibiansky, G. W. Milton, and J. G. Berryman, "On the effective viscoelastic moduli of two-phase media. III. Rigorous bounds on the complex shear modulus in two dimensions, in: Proc. R. Soc. Lond., Part A, 455, 2117-2149 (1999).
17. W. Jones and V. Thorn, Continued Fractions, Addison-Wesley Publishing Company, Massachusetts (1980).
18. A. A. Kaminsky and G. V. Gavrilov, "Subcritical stable growth of a penny-shaped crack in an aging viscoelastic orthotropic material with cylindrical anisotropy, Int. Appl. Mech., 43, No. 1, 68-78 (2007).
19. A. A. Kaminsky and M. F. Selivanov, "Growth of a penny-shaped crack with a nonsmall fracture process zone in a composite, " Int. Appl. Mech., 44, No. 8, 866-871 (2008).
20. A. A. Kaminsky and M. F. Selivanov, "On the application of branched operator continued fractions for a boundary problem of linear viscoelasticity, " Int. Appl. Mech., 42, No. 1, 115-126 (2006).
21. J. Li and G. J. Weng, "Strain-rate sensitivity, relaxation behavior, and complex moduli of a class of isotropic viscoelastic composites" ASME, J. Eng. Mater. Technol., 116, 495-504 (1994).
22. J. Li and G. J. Weng, "Anisotropic stress-strain relations and complex moduli of viscoelastic composite with aligned inclusions, " Comp. Eng., 4, 1073-1097 (1994).
23. Yu. A. Rossikhin and M. V. Shitikova, "Analysis of rheological equations involving more than one fractional parameters by the use of the simplest mechanical systems based on these equations, " Mech. Time-Dependent Mater., 5, 131-175 (2001).
24. M. F. Selivanov and Yu. A. Chernoivan, "A combined approach of the Laplace transform and Padé approximation to solving viscoelasticity problems, " Int. J. Solids Struct., 44, 66-76 (2007).
25. J. Stoer, "A direct method for Chebyshev approximation by rational functions, " Assoc. Comp. Mech., 11, No. 1, 59-69 (1964).
26. P. P. Valko and J. Abate, "Numerical Laplace inversion in rheological characterization, " J. Non-Newtonian Fluid Mech., 116, 395-406 (2004). (Pubitemid 38381736)