Certificate of Registration Media number Эл #ФС77-53688 of 17 April 2013. ISSN 2308-6033. DOI 10.18698/2308-6033
  • Русский
  • Английский

Modeling of viscoelastic foams characteristics based on the multiscale finite-element analysis

Published: 21.10.2016

Authors: Dimitrienko Yu.I., Dimitrienko I.D., Sborshikov S.V.

Published in issue: #11(59)/2016

DOI: 10.18698/2308-6033-2016-11-1555

Category: Mechanics | Chapter: Mechanics of Deformable Solid Body

The purpose of the research was to develop a method for calculating viscoelastic foams characteristics at steady cyclical fluctuations. The method is based on the theory of asymptotic averaging of periodic structures. We stated local viscoelasticity problems on the periodicity cell. The method developed allows us to calculate a complete set of components of the tensor of complex foams moduli of elasticity in a given frequency range. An example of a numerical simulation of viscoelastic foams characteristics shows that viscoelastic foams properties characterized by loss-angle tangent of the complex moduli of elasticity can be multiextremal by nature, with the presence of several critical frequencies. Furthermore, we give an example of a three-dimensional finite-element calculation of fields of the microstrain concentration tensors in the walls of the foam. For FEM calculations we used specialized software developed at the Department of Computational Mathematics and Mathematical Physics of Bauman Moscow State Technical University.

[1] Kobelev V.N., Kovarskiy L.M., Timofeev S.I. Raschet trekhsloynykh konstruktsiy [Calculation of three-layer structures]. Moscow, Mashinostroenie Publ., 1984, 300 p.
[2] Zhu H.X., Knott J.F., Mills N.J. Analysis of the elastic properties of open-cell foams with tetrakaidecahedral cells. J. Mech. Phys. Solids, 1997, vol. 45, pp. 319-343.
[3] Szyniszewski S.T., Smith B.H., Hajjar J.F., Schafer B.W., Arwade S.R. The mechanical properties and modeling of a sintered hollow sphere steel foam. Materials and Design, 2014, vol. 54, pp. 1083-1094.
[4] Ilyushin A.A., Pobedriya B.E. Osnovy matematicheskoi teorii termoviazkouprugosti [Fundamentals of mathematical thermoviscoelasticity theory]. Moscow, Nauka Publ., 1970, 356 p.
[5] Pobedrya B.E., Dimitrienko Yu.I. Uspekhi mekhaniki - Achievements in mechanics, 1987, iss. 10, no. 2, pp. 97-137.
[6] Hashin Z. Viscoelastic behavior of heterogeneous media. J. Appl. Mech. Trans. ASME.32E. 1965, pp. 630-636.
[7] Christensen R.M. Theory of viscoelasticity, 2nd ed. New York, Academic Press, 1982, 356 p.
[8] Imaoka Sh. Analyzing Viscoelastic materials. ANSYS Advantage, 2008, vol. 2, no. 4, pp. 46-47.
[9] 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.
[10] Dimitrienko Yu.I., Limonov V.A. Mekhanika kompozitnykh materialov - Mechanics of Composite Materials, 1988, no. 5, pp. 797-805.
[11] Dimitrienko Yu.I., Gubareva E.A., Sborschikov S.V Inzhenernyy zhurnal: nauka i innovatsii - Engineering Journal: Science and Innovation, 2014, iss. 4 (28). Available at:
[12] Dimitrienko Yu.I., Gubareva E.A., Sborschikov S.V. Matematicheskoe modelirovanie i chislennye metody - Mathematical Modeling and Computational Methods, 2014, no. 2, pp. 28-49.
[13] Dimitrienko Yu.I. Mekhanika sploshnoi sredy. V 4 tomakh. Tom 4. Osnovy mekhaniki tverdykh sred [Continuum mechanics. In 4 vols. Vol. 4. Fundamentals of solid mechanics]. Moscow, BMSTU Publ., 2013, 624 p.
[14] Dimitrienko Yu.I., Kashkarov A.I., Makashov A.A. Vestnik MGTU im. N.E. Baumana. Ser. Estestvennye nauki - Herald of Bauman Moscow State Technical University. Series Natural Sciences, 2007, no. 1, pp. 102-116.
[15] Pobedrya B.E. Mekhanika kompozitsionnykh materialov [Mechanics of composite materials]. Moscow, Lomonosov MSU Publ., 1984.
[16] Dimitrienko Yu.I., Dimitrienko I.D., Sborschikov S.V. Multiscale Hierarchical Modeling of Fiber Reinforced Composites by Asymptotic Homogenization Method. Applied Mathematical Sciences, 2015, vol. 9, no. 145, рр. 7211-7220. Available at: URL:
[17] Dimitrienko Yu.I. Mekhanika sploshnoi sredy. V 4 tomakh. Tom 1. Tenzornyy analiz [Continuum Mechanics. In 4 vols. Vol. 1. Tensor analysis]. Moscow, BMSTU Publ., 2011, 463 p.
[18] Bakhvalov N.S., Panasenko G.P. Osrednenie protsessov v periodicheskikh sredakh [Averaging processes in periodic media]. Moscow, Nauka Publ., 1984, 352 p.
[19] Sanches-Palensiya E. Neodnorodnye sredy i teoriya kolebaniy [Heterogeneous media and vibration theory]. Moscow, Mir Publ., 1984, 472 p.