Estimates of Dielectric Permeability of a Composite with Inclusions in the Form of Rotation Ellipsoids

For a composite with dispersed inclusions in the form of rotation ellipsoids we successively made estimates of dielectric permeability by means of a mathematical model of a representative element of the composite structure. Moreover, we applied the method of self-consistent field and used the dual variational formulation of a problem of electrostatics in a heterogeneous solid. We carried out a quantitative analysis of the calculated dependences allowing us to predict the effective values of dielectric permeability of composites with an ordered arrangement of the inclusions and in the case of their random orientation.

References

[1] Tareev B.M. Fizika dielektricheskikh materialov [Physics of dielectrics]. Moscow, Ener-goatomizdat Publ., 1982. 320 p.

[2] Vinogradov A.P. Elektrodinamika kompozitnykh materialov [The electrodynamics of composites]. Moscow, Editorial URSS Publ., 2001. 208 p.

[3] Trofimov N.N., ed. Fisika kompozitsionnykh materialov. V 2 t. T. 2 [Physics of composites. In 2 vol. Vol. 2]. Moscow, Mir Publ., 2005. 344 p.

[4] Politekhnicheskiy slovar’. A.Yu. Ishlinskiy, ed. [Polytechnic Dictionary]. Moscow, Sov. Entsiklopediya Publ., 1989. 656 p.

[5] Kats E.A. Fullereny, uglerodnye nanotrubki i nanoklastery. Rodoslovnaya form i idey [Fullerenes, carbon nanotubes and nanoclusters. Pedigree of forms and ideas]. Moscow, LKI Publ., 2008. 296 p.

[6] Sazhin B.I., ed. Elektricheskie svoystva polimerov [Electric properties of polymers]. Leningrad, Khimiya Publ., 1986. 224 p.

[7] Landau L.D., Lifshitz E.M. Electrodynamics of continuous media (Vol. 8. Course of theoretical physics). Pergamon Press, 1960.

[8] Dimitrienko Yu.I., Sokolov A.P., Markevich M.N. Modeling of dielectric properties of composite materials on the basis of asymptotic averaging. Nauka i obrazovanie. MGTU im. N.E. Baumana [Science & Education of the Bauman MSTU. Electronic Journal], 2013, no. 1. DOI: 10.7463/0113.0531682 Available at: http://technomag.bmstu.ru/en/doc/531682.html

[9] Fokin A.G., Shermergor T.D. Permittivity of heterogeneous materials. Zh. Tekh. Fiz. [Tech. Phys. The Russ. J. Appl. Phys.], 1969, vol. 39, no. 7, pp. 1308-1313 (in Russ.).

[10] Hashin Z., Strikman S. Variational approach to the theory of the effective magnetic permeability of multiphase materials. J. Appl. Phys., 1962, vol. 33, pp. 3125-3132. DOI: 10.1063/1.1728579

[11] Ermakov G.A., Fokin A.G., Shermergor T.D. Calculating the boundaries for the effective dielectric constants of inhomogeneous dielectrics. Zh. Tekh. Fiz. [Tech. Phys. The Russ. J. Appl. Phys], 1974, vol. 44, no. 2, pp. 249-255 (in Russ.).

[12] Zarubin V.S., Kuvyrkin G.N., Pugachev O.V. Variational approach to the estimate of the permittivity of a composite with dispersed inclusions. Mat. i mat. model. [Mathematics & Mathematical Modelling of the Bauman MSTU. Electronic Journal], 2015, no. 2. DOI: 10.7463/mathm.0215.0769483 Available at: http://mathmjournal.ru/en/index.html

[13] Zarubin V.S., Kuvyrkin G.N. Matematicheskie modeli mekhaniki i elektrodinamiki sploshnoy sredy [Mathematical models of mechanics and electrodynamics of continuous media]. Moscow, MGTU im. N.E. Baumana Publ., 2008. 512 p.

[14] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. Evaluation of dielectric permittivity of composite with dispersed inclusions. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Priborostr. [Herald of the Bauman Moscow State Tech. Univ., Instrum. Eng.], 2015, no. 3, pp. 50-64 (in Russ.). DOI: 10.18698/0236-3933-2015-3-50-64

[15] Zarubin V.S., Kuvyrkin G.N. Effective coefficients of thermal conductivity of a composite with ellipsoidal inclusions. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2012, no. 3, pp. 76-85 (in Russ.).

[16] Carslaw H.S., Jaeger J.C. Conduction of heat in solids. London, Oxford University Press, 1959.

[17] Zarubin V.S., Savel’eva I.Yu. Effective thermal conductivity coefficients of the composites with spheroidal inclusions. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2013, no. 4, pp. 116-126 (in Russ.).

[18] Zarubin V.S., Kuvyrkin G.N., Savel’eva I.Yu. Effective coefficients of thermal conductivity of a composite with prolate spheroid inclusions. Teplovye protsessy v tekhnike [Thermal Processes in Engineering], 2013, vol. 5, no. 6, pp. 276-282 (in Russ.).

[19] Hill R. A self-consistent mechanics of composite materials. J. Mech. Phys. Solids, 1965, vol. 13, no. 4, pp. 213-222.

[20] Golovin N.N., Zarubin V.S., Kuvyrkin G.N. Mixture models of composite mechanics. P. 1. Thermal mechanics and thermoelasticity of multicomponent mixture. Vestn. Mosk. Gos. Tekh. Univ. im. N.E. Baumana, Estestv. Nauki [Herald of the Bauman Moscow State Tech. Univ., Nat. Sci.], 2009, no. 3, pp. 36-49 (in Russ.).