539.3 Modeling of effective relaxation and creep kernels of viscoelastic composites by asymptotic averaging method

Dimitrienko Y. I. (Bauman Moscow State Technical University), Yurin Y. V. (Bauman Moscow State Technical University), Sborschikov S. V. (Bauman Moscow State Technical University), Yakhnovskiy A. D. (Bauman Moscow State Technical University), Baymurzin R. R. (Bauman Moscow State Technical University)

COMPOSITES, VISCOELASTICITY, RELAXATION KERNELS, CREEP KERNELS, COMPLEX ELASTIC MODULI, UNIDIRECTIONAL COMPOSITES, ASYMPTOTIC AVERAGING METHOD, FINITE ELEMENT METHOD, NUMERICAL SIMULATION


doi: 10.18698/2309-3684-2020-3-2246


The problem of calculating the integral characteristics of the viscoelasticity of composite materials is considered, based on information on similar characteristics of the composite components and its microstructure. An algorithm is proposed for predicting the effective relaxation and creep kernels of composites with an arbitrary reinforcement microstructure. The algorithm is based on the Fourier transform application and the inverse Fourier transform, as well as the method of asymptotic averaging for composites under steady-state polyharmonic vibrations. The algorithm uses exponential relaxation and creep kernels for the initial components of the composite. The basis of the computational procedure of the proposed algorithm is the finite element solution of local viscoelasticity problems over the composite periodicity cell. The result of the algorithm application is the determination of the exponential relaxation and creep kernels parameters for composite materials, which makes it possible to obtain a problem solution in a completely closed form. As an example, a numerical simulation of the viscoelastic-tic characteristics of unidirectionally reinforced carbon /epoxy composites has been carried out. It is shown that the developed algorithm allows one to obtain effective relaxation and creep kernels of the composite with high accuracy, without oscillations, which, as a rule, ac-company the methods of inverting Fourier transforms.


[1] Shapery R. Viscoelastic behavior and analysis of composite materials. Mechanics of Composite Materials, 1974, vol. 4, pp. 85–168.
[2] Hashin Z. Complex moduli of viscoelastic composites: I. General theory and application to particulate composites. International Journal of Solids and Structures, 1970, vol. 6, no. 5, pp. 539–552.
[3] Chen C.P., Lakes R.S. Analysis of high loss viscoelastic composites. Journal Materials Science, 1993, vol. 28, pp. 4299–4304.
[4] Friebel C., Doghri I., Legat V. General mean-field homogenization schemes for viscoelastic composites containing multiple phases of coated inclusions. International Journal of Solids and Structures, 2006, vol. 43, pp. 2513–2541.
[5] Shibuya Y. Evaluation of creep compliance of carbon-fiber-reinforced composites by homogenization theory. JSME International Journal Series A Solid Mechanics and Material Engineering, 1997, vol. 40, pp. 313–319.
[6] Haasemann G, Ulbricht V. Numerical evaluation of the viscoelastic and viscoplastic behavior of composites. Technische Mechanik, 2010, vol. 3, no. 1–3, pp. 122–135.
[7] 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, 2013, vol. 2, no. 2, pp. 11–18.
[8] Tran A.B., Yvonnet J., He Q.–C., Toulemonde C., Sanahuja J. A simple computational homogenization method for structures made of linear heterogeneous viscoelastic materials. Computer Methods in Applied Mechanics and Engineering, 2011, vol. 200, pp. 2956–2970.
[9] Matzenmiller A, Gerlach S. Micromechanical modeling of viscoelastic composites with compliant fiber–matrix bonding. Computational Materials Science, 2004, vol. 29, iss. 3, pp. 282–300.
[10] Imaoka S. Analyzing Viscoelastic materials. Ansys Advantage, 2008, vol. 2, no. 4, pp. 46–47.
[11] Cavalcante M.A.A., Marques, S.P.C. Homogenization of periodic materials with viscoelastic phases using the generalized FVDAM theory. Computational Materials Science, 2014, vol. 87, pp. 43–53.
[12] Dimitrienko Y.I., Gubareva E.A., Sborschikov S.V. Finite element modulation of effective viscoelastic properties of unilateral composite materials. Маthematical Modeling and Computational Methods, 2014, no. 2, pp. 28–48.
[13] Maksimov R.D., Plume E.Z. Creep in unidirectionally reinforced polymer composites. Mechanics of Composite Materials, vol. 20, no. 2, pp. 149–157.
[14] Pobedrya B.E. Mekhanika kompozitsionnykh materialov [Mechanics of composite materials]. Moscow, Lomonosov Moscow State University Publ., 1984, 324 p.
[15] Il'yushin A.A., Pobedrya B.E. Osnovy matematicheskoj teorii termovyazkouprugosti [Fundamentals of the mathematical theory of thermovyazcoelasticity]. Moscow, Nauka Publ., 1970, 356 p.
[16] Dimitrienko Y.I., Gubareva E.A., Yakovlev D.O. Asimptoticheskaya teoriya vyazkouprugosti mnogoslojnyh tonkih kompozitnyh plastin [Asymptotic theory of viscoelasticity of multilayer thin composite plates]. Nauka i obrazovanie: nauchnoe izdanie MGTU im. N.E. Baumana [Science and Education of Bauman MSTU], 2014, no. 10, pp. 359–382.
[17] Dimitrienko Y.I., Fedonyuk N.N., Gubareva E.A., Sborshchikov S.V., Prozorovsky A.A. Mnogomasshtabnoe konechno-elementnoe modelirovanie trekhslojnyh sotovyh kompozitnyh konstrukcij [Multiscale finite element modeling of three-layer honeycomb composite structures]. Nauka i obrazovanie: nauchnoe izdanie MGTU im. N.E. Baumana [Science and Education of Bauman MSTU], 2014, no. 7, pp. 243–265.
[18] Dimitrienko Yu.I., Fedonyuk N.N., Gubareva E.A., Sborshchikov S.V., Prozorovsky A.A., Erasov V.S., Yakovlev N.O. Modeling and development of three-layer sandwich composite materials with honeycomb core. Herald of the Bauman Moscow State Technical University, Series Natural Sciences, 2014, no. 5, pp. 66–82.
[19] Dimitrienko Y.I., Gubareva E.A., Yurin Y.V. Asymptotic theory of thermocreep for multilayer thin plates. Маthematical Modeling and Computational Methods, 2014, no. 4, pp. 18–36.
[20] Dimitrienko Y.I., Gubareva E.A., Sborschikov S.V. Asymptotic theory of constructive-orthotropic plates with two-periodic structures. Маthematical Modeling and Computational Methods, 2014, no. 1, pp. 36–56.
[21] Bakhvalov N.S., Panasenko G.P. Osrednenie protsessov v periodicheskikh sredakh. Matematicheskie zadachi mekhaniki kompozitsionnykh materialov [Averaging processes in periodic media. Mathematical problems of the compo­site material mechanics]. Moscow, Nauka Publ., 1984, 352 p.
[22] Moskvitin B.V. Soprotivlenie vyazkouprugih materialov [Resistance of viscoelastic materials]. Moscow, Nauka Publ., 1972, 328 p.
[23] Christensen R.M. Theory of Viscoelasticity — 2nd Edition. New York, Academic Press, 1982, 356 p.
[24] Dimitrienko Yu. I. Mekhanika sploshnoy sredy. Tom 4. Osnovy mekhaniki tver­dogo tela [Continuum Mechanics. Vol. 4. Fundamentals of solid mechanics]. Moscow, BMSTU Publ., 2013, 624 p.
[25] Dimitrienko Yu.I. Mekhanika sploshnoj sredy. T. 1. Tenzornyj analiz [Continuum Mechanics. Vol. 1. Tensor analysis]. Moscow, BMSTU Publ., 2011, 367 p.
[26] Rabotnov Yu.N. Elementy nasledstvennoj mekhaniki tvyordyh tel [Elements of hereditary mechanics of solids]. Moscow, Nauka Publ., 1977, 384 p.
[27] Gorshkov A.G., Starovoitov E I., Yarovaya A.V. Mekhanika sloistyh vyazko-uprugoplasticheskih elementov konstrukcij [Mechanics of layered viscoelastic structural elements]. Moscow, Fizmatlit Publ., 2005, 576 p.
[28] Malmeister A.K., Tamuzh V.P., Teters G.A. Soprotivlenie polimernyh i kompozitnyh materialov [Resistance of polymer and composite materials]. Riga, Zinatne Publ., 1980, 572 p.
[29] Certificate no. 2018614767 Programma MultiScale_SMCM dlya mnogomasshtabnogo modelirovaniya napryazhenno-deformirovannogo sostoyaniya konstrukcij iz kompozicionnyh materialov, na osnove metoda mnogourovnevoj asimptoticheskoj gomogenizacii i konechno-elementnogo resheniya trekhmernyh zadach teorii uprugosti [MultiScale_SMCM program for multiscale modeling of the stress-strain state of structures made of composite materials, based on the method of multilevel asymptotic homogenization and finite element solution of three-dimensional problems of elasticity theory]: certificate of ofic. registration of computer programs/ Yu.I. Dimitrienko, S.V. Sborshchikov, Yu.V. Yurin; applicant and copyright holder: BMSTU — no. 2018677684; application 21.02.2018; registered in the register of computer programs 17.04.2018 — [1].


Димитриенко Ю.И., Юрин Ю.В., Сборщиков С.В., Яхновский А.Д., Баймурзин Р.Р. Моделирование эффективных ядер релаксации и ползучести вязко-упругих композитов методом асимптотического осреднения. Математическое моделирование и численные методы, 2020, № 3, с. 22–46.



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