539.3 Modeling nonlinear dielectric properties of composites based on the asymptotic homogenization method
Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Zubarev K. M. (Bauman Moscow State Technical University)
NUMERICAL MODELING, FINITE ELEMENT METHOD, ASYMPTOTIC AVERAGING METHOD, TEXTILE COMPOSITES, TWILL WEAVE, PLAIN WEAVE, UNIDIRECTIONAL COMPOSITES, HIGH TEMPERATURES, THERMAL DESTRUCTION, POLYMER PHASE, PYROLYTIC PHASE, AMORPHOUS PHASE, CRYSTALLINE PHASE, ELASTIC CHARACTERISTICS, MICROSTRESSES
doi: 10.18698/2309-3684-2020-2-2645
The paper is devoted to the development of a method for calculating the nonlinear dielectric properties of composites with a periodic structure. Methods for predicting of the nonlinear dielectric properties of composites play an important role in the design of dielectric materials with specified properties, in particular for heterogeneous ferroelectrics, which are widely used to create various devices and electrical devices, for example, to create memory storage devices for computers. A quasi-static problem of the distribution of an electric charge in an inhomogeneous polarizable medium with a periodic structure and nonlinear dielectric properties is considered. To solve this nonlinear problem, the asymptotic homogenization method proposed by N.S. Bakhvalov, E. Sanchez-Palencia, B.E. Pobedria. As a result, local nonlinear problems of electrostatics on the periodicity cell are formulated, an algorithm for calculating effective nonlinear constitutive relations for dielectric properties, and an averaged problem for a composite with effective properties are proposed. For the case of a composite with a layered structure, the solution of local problems is obtained, and effective defining relations for the nonlinear dielectric properties of the composite are constructed. It is shown that a laminated composite is a transversely isotropic nonlinear dielectric material if it is isotropic materials. A numerical example of calculating the nonlinear properties of a 2-layer composite based on barium titanate and ferroelectric ceramic varicond VK4 is considered. A model is proposed that describes the nonlinear dependence of the dielectric constant of these materials on the vector of the electric field strength. It is shown that the nonlinear dependence of the dielectric constant tensor of the composite on the strength vector differs significantly for the direction of the field in the plane of the layers and in the transverse direction. It is shown that the developed technique can serve as a basis for designing nonlinear dielectric composite materials with anisotropic properties.
[1] Iona F., Shirane D. Segnetoelektricheskie kristally [Ferroelectric crystals]. Moscow, Mir Publ., 1965, 555 p.
[2] Strukov V.A. Segnetoelektrichestvo [Ferroelectricity]. Moscow, Nauka Publ., 1979, 96 p.
[3] Berman L.S. Simulation of hysteresis in a metal – ferroelectric – semiconductor structure. Semiconductors, 2001, vol. 34, iss. 2, pp. 193–195.
[4] Garevskij V.N., Novikov I.L., Dikareva R.P., Romanova T.S. Materialo-vedenie. Konstrukcionnye i elektrotekhnicheskie materialy. Materialy i elementy elektronnoj tekhniki. Metodicheskie ukazaniya k laborator-nym rabotam №1-4 dlya studentov II kursa EMF, REF. [Material Science. Structural and electrical materials. Materials and elements of electronic equipment. Guidelines for laboratory work No. 1-4 for students of the second year of EMF, REF.] Novosibirsk, NSTU Publ., 2009, 74 p.
[5] Chen Z., Wang X., Ringer S.P., Liao X. Manipulation of nanoscale domain switching using an electron beam with omnidirectional electric field distribution. Physical Review Letters, 2016, vol. 117, art. no. 027601. DOI: https://doi.org/10.1103/PhysRevLett.117.027601
[6] 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.
[7] Pobedrya B.E. Mekhanika kompozitsionnykh materialov [Mechanics of composite materials]. Moscow, Lomonosov Moscow State University Publ., 1984, 324 p.
[8] Sanchez-Palencia E. Non-Homogeneous Media and Vibration Theory. New York, Springer Publ., 1980.
[9] Dimitrienko Yu.I. Mekhanika kompozicionnyh materialov pri vysokih temperaturah [Mechanics of composite materials at high temperatures]. Moscow, Mashinostroenie Publ., 1997, 356 p.
[10] Dimitrienko Yu.I., Kashkarov A.I. Finite element method of calculation of efficient characteristics of composites with periodical structure. Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2002, no. 2, pp. 95–107.
[11] 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, pp. 7211–7220.
[12] Dimitrienko Yu.I., Fedonyuk N.N., Gubareva E.A., Sborschikov S.V., Prozorovskiy 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. 66–81.
[13] Dimitrienko Yu. I., Gubareva E. A., Yurin Yu. V. Asymptotic theory of thermal creep of multilayer thin plates. Mathematical modeling and Computational Methods, 2014, no. 4 (4), pp. 18–36.
[14] Dimitrienko Yu.I., Gubareva E.A., Markevich M.N., Sborshchik S.V. Mathematical modelling of dielectric properties of nanostructural composites using asymptotic homogenizing method. Herald of the Bauman Moscow State Technical University. Series Natural Sciences, 2016, no. 1, pp. 76–89.
[15] Dimitrienko Yu.I., Zubarev K.M., Yurin Yu.V., Yakovlev V.I. Modeling of the electromagnetic and elastic properties of composite materials. IOP Conference Series: Material Science and Engineering, 2020, vol. 934, art. no. 012016. DOI:10.1088/1757-899X/934/1/012016
[16] 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.
[17] Dimitrienko Yu.I. Mekhanika sploshnoy sredy. Tom 2. Universalnye zakony mekhaniki i elektrodinamiki sploshnoy sredy [Continuum Mechanics. Vol. 2. Universal laws of continuous media mechanics and electrodynamics]. Moscow, BMSTU Publ., 2011, 560 p.
[18] Dimitrienko Yu.I. Tenzornoe ischislenie [Tensor calculus]. Moscow, Vysshaya shkola Publ., 2001, 576 p.
[19] Bulybenko V.Yu. Varikondy v elektronnyh impul'snyh skhemah [Variconds in electronic pulse circuits]. Moscow, Sovetskoe Radio Publ., 1971, 271 p.
[20] Okazaki K. Tekhnologiya keramicheskih dielektrikov [Technology of ceramic dielectrics]. Moscow, Energia Publ., 1976, 327 p.
[21] Variconds [Electronic resource]. Museum of Electronic Rarities. 2006. URL: www.155la3.ru/varikond.htm (date accessed: 06.01.2020).
[22] Koritsky Yu.V., Pasynkov V.V., Tareev B.M. Spravochnik po elektrotekhnicheskim materialam. Tom 3. [Handbook of electrotechnical materials. Vol. 3.] Leningrad, Energoatomizdat Publ., 1988, 728 p.
Димитриенко Ю.И., Губарева Е.А., Зубарев К.М. Моделирование нелинейных диэлектрических свойств композитов на основе метода асимптотической гомогенизации. Математическое моделирование и численные методы. 2020. № 2. с. 26–45
Download article
Количество скачиваний: 439