539.3 Modeling the effective characteristics of transversely isotropic incompressible composites with finite strains
Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Karimov S. B. (Bauman Moscow State Technical University), Kolzhanova D. Y. (Bauman Moscow State Technical University)
LAYERED COMPOSITES, INCOMPRESSIBLE MEDIA, TRANSVERSELY ISOTROPIC MEDIUM, FINITE STRAINS, ASYMPTOTIC HOMOGENIZATION METHOD, UNIVERSAL MODELS OF ELASTIC MEDIA, ENERGY TENSOR PAIRS
doi: 10.18698/2309-3684-2018-4-7292
The paper considers a model of effective constitutive relations for a transversal-isotropic incompressible composite with finite strains. The model belongs to the so-called class of universal models that connect several pairs of energy stress and strain tensors simultaneously. A method is proposed for separating coupled problems of micro- and macroscopic deforming composites with finite strains that arise when the method of asymptotic homogenization (AH) of periodic structures is used. The method is based on the application of the effective constitutive relation model as an approximation dependence of the results of numerical simulation of the composite deformation curves obtained using the exact AH method. To find the elastic constants of the transversely isotropic composite model the method of minimizing the deviation of the approximation of deformation diagrams from the AH diagrams is used for a series of problems of standard deforming at finite strains. To solve minimization problems, the Nelder—Mead method is used. The results of numerical simulation by the proposed method for nonlinear elastic layered composites are presented, which showed good approximation accuracy, achieved due to application of the proposed method for the separation of coupled problems of micro- and macroscopic deforming.
[1] Bakhvalov N.S., Panasenko G.P. Osrednenie protsessov v periodicheskikh sredakh [Averaging processes in periodic media]. Moscow, Nauka Publ., 1984, 352 p.
[2] Bensoussan A., Lions JL., Papanicalaou G. Asymptotic analysis for periodic structures. Amsterdam, New York, North-Holland Co. Publ., 1978, 396 p.
[3] Pobedrya B.E. Mekhanika kompozitsionnykh materialov [Mechanics of composite materials]. Moscow, Lomonosov Moscow State University Publ., 1984, 324 p.
[4] Sanchez-Palencia E. Non-Homogeneous Media and Vibration Theory. New York, Springer Publ., 1980.
[5] Christensen, R.M. Mechanics of composite materials. New York, John Wiley & Sons Publ., 1979. 324 p.
[6] Dimitrienko Yu.I. Composites Science and Technology, 1999, vol. 59, no. 7,
pp. 1041–1053.
[7] Dimitrienko Yu.I., Gubareva E.A., Sborshchikov S.V. Matematicheskoe mode-
lirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 2, pp. 28–48.
[8] Dimitrienko Yu.I., Fedonyuk N.N., Gubareva E.A., Sbornikov S.V., Prozorovsky A.A. Nauka i obrazovanie: electronnyy nauchno-tekhnicheskiy zhurnal — Science and Education: Electronic Scientific and technical Journal, 2014, no. 10.
DOI: 10.7463 / 1014.0730105
[9] Dimitrienko Iu.I., Yakovlev N.O., Erasov V.S., Fedonuk N.N., Sborshchikov S.V., Gubareva E.A., Krylov V.D., Grigoryev M.M., Prozorovsky A.A. Kompozity
i nanostruktury – Composites and Nanostructures, 2014, vol. 6, no. 1, pp. 32–48.
[10] Dimitrienko Iu.I., Gubareva E.A., Sborshchikov S.V. Matematicheskoe mode-
lirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2014, no. 1, pp. 36–57.
[11] Dimitrienko Yu.I., Yakovlev D.O. Mekhanika kompozitsionnykh materialov i konstruktsiy – Mechanics of Composite Materials and Structures, 2014, vol. 20, no. 2, pp. 260–282.
[12] Dimitrienko Yu.I., Kashkarov A.I. Vestnik MGTU im. N.E. Baumana. Seria Estestvennye nauki – Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2002, no. 2, pp. 95–108.
[13] Dimitrienko Yu.I., Drogolub A.N., Gubareva E.A. Nauka i obrazovanie: elec-tronnyy nauchno-tekhnicheskiy zhurnal – Science and Education: Electronic Scientific and technical Journal, 2015, no. 2.
DOI: 10.7463/0215.0757079 http://technomag.bmstu.ru/doc/757079.html
[14] Dimitrienko Yu.I. Izvestiya vysshikh uchebnykh zavedeniy. Mashinostroenie — Proceedings of Higher Educational Institutions. Маchine Building, 2015,
no. 11, pp. 68–77. DOI: 10.18698/0536-1044-2015-11-68-77
[15] Dimitrienko Yu.I., Gubareva E.A., Kolzhanova D.Yu. Inzhenernyy zhurnal: Nauka i innovatsii – Engineering Journal: Science and Innovation, 2015,
no. 5 (29). DOI: 10.18698/2308-6033-2015-5-1405
[16] Dimitrienko Yu.I, Gubareva E.A., Kolzhanova D.Yu., Karimov S.B. Ma-tematicheskoe modelirovanie i chislennye metody — Mathematical Modeling and Computational Methods, 2017, no. 1, pp. 32–54.
DOI: 10.18698/2309-3684-2017-1-3254
[17] Qingsheng Yang, Fang Xu. Frontiers of Mechanical Engineering in China. 2009, vol. 4, no. 3, pp. 284–288.
[18] Aboudi J., International Journal of Multiscale Computational Engineering, 2008, no. 6, pp. 411–434.
[19] Bin Zhang, Xiaoming Yu and Boqin Gu. Polymer Composites, 2015. DOI: 10.1002/pc.23596
[20] Ge Q., Luo X., Iversen C.B., Nejad H.B., Mather P.T., Dunn M.L., Qi H.J. Inter-national Journal of Solids and Structures, 2014, vol. 51, pp. 2777–2790.
[21] Dimitrienko Yu.I., Dashtiev I.Z. Vestnik MGTU im. N.E. Baumana. Seria Estestvennye nauki – Herald of the Bauman Moscow State Technical University. Series: Natural Sciences, 2001, no. 1, pp. 21–41.
[22] Dimitrienko Yu.I. Mekhanika sploshnoy sredy. V 4 tomakh. T. 2. Universalnye zakony mekhaniki i elektrodinamiki sploshnykh sred [Continuum Mechanics.
In 4 vols. Vol. 2. Universal lows of continuum mechanics and electrodynamics]. Moscow. BMSTU Publ., 2011, 560 p.
Димитриенко Ю.И., Губарева Е.А., Каримов С.Б., Кольжанова Д.Ю. Модели-рование эффективных характеристик трансверсально-изотропных несжимаемых композитов с конечными деформациями. Математическое моделирование и чис-ленные методы, 2018, № 4, с. 72–92.
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