539.3 Finite element modulation of effective viscoelastic properties of unilateral composite materials

Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University)

COMPOSITES, VISCOELASTICITY, STABLE-STATE VIBRATIONS, COMPLEX ELASTICITY MODULUS, UNILATERAL COMPOSITES, ASYMPTOTIC AVERAGING METHOD, FINITE ELEMENT METHOD, LOSS TANGENT, NUMERICAL SIMULATION


doi: 10.18698/2309-3684-2014-2-2848


We propose a method for calculating effective viscoelastic properties of composite materials under steady-state cyclical vibrations. The method is based on asymptotic averaging of periodic structures and finite-element solution of local problems of viscoelasticity in periodicity cells of composite materials. We provide examples of numerical simulation of viscoelastic properties for composites with unidirectional reinforcement, and of calculations of complex tensors of stress concentration in a periodicity cell. The paper presents a comparative analysis of dependencies of loss tangent of complex composite elasticity
modulus on vibration frequencies obtained through FEA calculations and rough mixed formulae. We show that rough mixed formulae, often used for calculating dissipative properties of composite materials, can yield appreciable calculation errors.


[1] Dimitrienko Yu.I., Yakovlev N.O, Erasov V.S., Fedonyuk N.N., Sborschikov S.V., Gubareva E.A., Krylov V.D., Grigor`ev M.M., Prozorovskiy A.A. Komposity i nanostruktury — Composites and Nanostructures, 2014, no. 1, vol. 6, pp. 32–48.
[2] Dimitrienko Yu.I, Fedonyuk N.N., Gubareva E.A., Sborschikov S.V, Prozorovsky A.A. Nauka i obrazovanie. Elektronnoe nauchno-tekhnicheskoe izdanie — Science and Education. Electronic Scientific and Technical Journal, 2014, no. 10. doi: 10.7464/1014.0730105
[3] Sheldon Imaoka. Analyzing Viscoelastic materials. ANSYS Advantage, 2008, vol. 2, no. 4, pp. 46–47.
[4] Matzenmiller A., Gerlach S. Micromechanical modeling of viscoelastic composites with compliant fiber–matrix bonding. Computational Materials Science, 2004, vol. 29, issue 3, pp. 283–300.
[5] Hashin Z. Viscoelastic behavior of heterogeneous media. J. Appl.Mech. Trans. ASME. 32E, 1965, pp. 630–636.
[6] Christensen R.M. Theory of viscoelasticity. 2nd ed. Academic Press, New York, 1982, 356 p.
[7] Bakhvalov N.S., . Panasenko G.P. Avaraging of Processes in Periodic Media. Moscow, Nauka Publ., 1984, 356 p.
[8] Pobedrya B.E. . Mechanics of Composite Materials. Moscow, Moscow State University Publ., 1984, 324 p.
[9] Dimitrienko Yu.I., Sokolov A.P. . Mathematical Modeling, 2012, no. 5, vol. 24, pp. 3–20.
[10] Dimitrienko Yu.I., Sborschikov S.V., Sokolov A.P., Shpakova Yu.I. Computational
Modeling of Failure of Textile Composites. Computational Continuum Mechanics, 2013, vol. 6, no. 4, pp. 389–402.
[11] Dimitrienko Yu.I., Limonov V.A. . Mechanics of Composite Materials, 1988, no. 5, pp. 797–805.
[12] Michel J.C., Moulinec H., Suquet P. Effective properties of composite materials with periodic microstructure: a computational approach. Comput. Methods Appl. Mech. Eng., 1999, vol. 172, pp. 109–143.
[13] Shibuya Y. Evaluation of creep compliance of carbon-fiber-reinforced composites by homogenization theory. JSME Int. J. Ser. A., vol. 40, 1997, pp. 313–319.
[14] Haasemann G., Ulbricht V. Numerical evaluation of the viscoelastic and viscoplastic behavior of composites. Technische Mechanik, 2010, vol. 30, no. 1–3, pp. 122–135.
[15] Masoumi S., Salehi M., Akhlaghi M. Nonlinear Viscoelastic Analysis of Laminated Composite Plates – A Multi Scale Approach. International Journal of Recent advances in Mechanical Engineering (IJMECH), 2013, vol. 2, no. 2, pp. 11–18.
[16] Pobedrya B.E., Dimitrienko Yu.I. Uspekhi Mehkaniki. Advance in Mechanics, 1987, no. 2, issue 10, pp. 97–137.
[17] Dimitrienko Yu.I. . Continuum Mechanics.In 4 vols. Vol. 4. Foundations of Mechanics
of Rigid Body. Moscow, BMSTU Publ., 2013, 624 p.
[18] Dimitrienko Yu.I. Continuum Mechanics.In 4 vols. Vol. 1. Tensor Analysis. Moscow, BMSTU Publ.,
2011, 463 p.
[19] Il`yushin A.A, Pobedrya B.E. Foundations of Mathematical Theory of Thermoviscoelasticity.
Moscow, Nauka Publ., 1970, 356 p.
[20] Dimitrienko Yu.I., Gubareva E.A., Sborschikov S.V. . Mathematical Modelling and Computational
Methods, 2014, no. 1, p. 36–57.
[21] Dimitrienko Yu.I., Sokolov A.P. Vestnik MGTU im. N.E. Baumana. Seriya Estestvennye Nauki. Herald of the Bauman Moscow State University. Series: Natural Sciences, 2008, no. 2, pp. 57–67.
[22] Dimitrienko Yu.I., Sokolov A.P. Informatsionnye tekhnologii . Information Technologies, 2008, no. 8, pp. 31–38.
[23] Dimitrienko Yu.I., Sborschikov S.V., Sokolov A.P., Sadovnichiy D.N., Gafarov B.R. Kompozity i nanostruktury. Composites and Nanostructures, 2013, no. 3, pp. 35–51.
[24] Dimitrienko Yu.I., Sborschikov S.V., Sokolov A.P. Mekhanika kompozitsionnykh
materialov i konstruktsii. Composit Mechanics and Design, 2013, no. 3, vol. 19, pp. 365–383.


Dimitrienko Y., Gubareva E., Sborschikov S. Finite element modulation of effective viscoelastic properties of unilateral composite materials. Маthematical Modeling and Coтputational Methods, 2014, №2 (2), pp. 28-48



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