15 / 16
Моделирование вязкоупругих характеристик пенопластов
…
Инженерный журнал: наука и инновации
# 11·2016 15
Modeling of viscoelastic foams characteristics
based on the multiscale finite-element analysis
© Yu.I. Dimitrienko, I.D. Dimitrienko, S.V. Sborschikov
Bauman Moscow State Technical University, Moscow, 105005, Russia
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 as-
ymptotic averaging of periodic structures. We stated local viscoelasticity problems on the
periodicity cell. The method developed allows us to calculate a complete set of compo-
nents 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 visco-
elastic foams properties characterized by loss-angle tangent of the complex moduli of
elasticity can be multiextremal by nature, with the presence of several critical frequen-
cies. 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 cal-
culations we used specialized software developed at the Department of Computational
Mathematics and Mathematical Physics of Bauman Moscow State Technical University.
Keywords:
viscoelastic characteristics, foam, multiscale modeling, method of asymptotic
averaging, complex moduli of elasticity, loss-angle tangent, finite-element method, nu-
merical simulation.
REFERENCES
[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.