A Three-Dimensional Numerical Analysis on the Effective Permittivity of Composites Including Ellipsoids

Abstract:

To investigate the effective permittivity of composites composed of ellipsoidal inclusions, three-dimension numerical models for ellipsoidal inclusions distributed randomly are built with the finite-element modeling software Comsol Multiphysics. After calculating the effective permittivity for different cases and comparing the results with analytical results from the Maxwell-Garnett mixing rule, we find that the finite-element method has an advantage in detecting details of the interaction among inclusions, which have some impacts on the effective permittivity and could not be accurately taken into account in the analytical model. The finite-element method is expected to solve more complex problems on electromagnetic computation.

• Periodical: Applied Mechanics and Materials (Volume 483)
• Pages: 23-27
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.483.23
• Online since: December 2013
• Authors: De Yuan Zhang, Li Ming Yuan*, Yong Gang Xu, Jun Cai
• Keywords: Effective Permittivity, Ellipsoidal Inclusions, Finite Element Method (FEM)

References

[1] J.M. Garnett, Colors in metal glasses and metal films, Transactions of the Royal Society, London, 1904, pp.385-420.

[2] D.A.G. Bruggeman, Berechnung verschiedener physikalischer Konstanten von heterogenen Substanzen.I. Dielektrizitätskonstanten und Leitfähigkeiten der Mischkörper aus isotropen Substanzen, Annalen der Physik 416 (1935) 636-664.

DOI: 10.1002/andp.19354160705

[3] A.H. Sihvola, J.A. Kong, Effective Permittivity of Dielectric Mixtures, IEEE T. Geosci. Remote 26 (1988) 420-429.

DOI: 10.1109/36.3045

[4] O. Levy, D. Stroud, Maxwell Garnett theory for mixtures of anisotropic inclusions: Application to conducting polymers, Phys. Rev. B 56(1997) 8035-8046.

DOI: 10.1103/physrevb.56.8035

[5] B. Drnovšek, V.B. Bregar, M. Pavlin, The effect of complex permeability and agglomeration on composite magnetic systems: A three-dimensional numerical analysis and comparison with analytical models, J. Appl. Phys. 103 (2008) 07D924.

DOI: 10.1063/1.2839580

[6] I. Krakovsky, V. Myroshnychenko, Modeling dielectric properties of composites by finite-element method, J. Appl. Phys. 92 (2002) 6743-6748.

DOI: 10.1063/1.1516837

[7] V. Myroshnychenko, C. Brosseau, Finite-element method for calculation of the effective permittivity of random inhomogeneous media, Phys. Rev. E 71 (2005) 016701.

DOI: 10.1103/physreve.71.016701

[8] Y.B. Sun, J.C. Han, Y.M. Zhang, Relative dielectric constant calculation model for three-phase porous composite materials, Comp. Mater. Sci. 45 (2009) 1125-1128.

DOI: 10.1016/j.commatsci.2009.01.012

[9] S.B. Jones, S.P. Friedman, Particle shape effects on the effective permittivity of anisotropicor isotropic media consisting of aligned or randomly oriented ellipsoidal particles, Water Resour. Res. 36 (2000) 2821-2833.

DOI: 10.1029/2000wr900198

[10] C. Brosseau, A. Beroual, A. Boudida, How do shape anisotropy and spatial orientation of the constituents affect the permittivity of dielectric heterostructures, J. Appl. Phys. 88 (2000) 7278-7288.

DOI: 10.1063/1.1321779

[11] S. Giordano, Effective medium theory for dispersions of dielectric ellipsoids, J. Electrostat. 58 (2003) 59-76.

DOI: 10.1016/s0304-3886(02)00199-7