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Fiber-reinforced composite materials are widely used in aeronautics and automotive industries due to their excellent mechanical properties. Composites with high conductive fibers embedded have good performance of shielding effectiveness and become possible candidates to replace metals. One approach for analyzing the electromagnetic (EM) interaction of fiber-reinforced composites is to use full numerical methods, which allow precise modeling and give accurate results. However, numerical methods may lead to prohibitive computational time and memory capacity due to the strong dependence on the shielding properties from heterogeneous microstructures.In composite materials, two important parameters, effective permittivity eff and effective permeability eff, determine the interaction between the electromagnetic field and the materials. For estimating the effective parameters, homogenization techniques have been developed to describe a composite mixture in terms of a spatially homogeneous electromagnetic response, mostly under static conditions. The well-known rules are the Maxwell-Garnett (MG) formula and the Bruggeman formula.These rules are usually applied to the dilute composite materials and provide satisfactory results as long as the wavelength remains large compared to the size of the heterogeneities. Recently, revised homogenization models have been developed to extend the frequency range. Some of them are presented with the help of numerical method but still require substantial computational time and resources to be performed. One recently proposed homogenization model, called dynamic homogenization model (DHM), is an extension of quasi-static homogenization methods for microwave frequencies. It is obtained by introducing a microstructure-dependent characteristic length for the composites made of a square array of circular cylinders buried in the matrix, based on the basic inclusion problems. The DHM overcomes the limitations of standard static homogenization tools, but only applicable to low fiber volume fraction (less than 20%).In this paper, we focus on the microstructure in the case of a square array of circular 2D conductive long fibers embedded in a dielectric matrix. A revised DHM is proposed to describe the effective permittivity of the composite materials with different inclusion concentrations, including higher fiber volume fraction. Firstly, an iterative procedure is employed to estimate an effective permittivity, which is then used to modify the wavelength in the DHM. Secondly, an empirical formula-based characteristic size of the microstructure is presented by considering the current distribution of the fibers under the EM wave illumination in the case of high fiber volume fractions. Therefore, the final modified homogenization model is given for the effective permittivity of composites with arbitrary inclusion concentrations. It can be used to efficiently calculate the reflection and transmission coefficients, as well as the shielding effectiveness by classical transmission-line methods. Three infinite sheets with different physical parameters are utilized for validation. We compare the results of the shielding effectiveness obtained from this homogenization model with those obtained from a full numerical solution of the actual fiber composites. Reasonable agreements obtained demonstrate that the proposed model could define the effective permittivity of the composites with high fiber concentration over a wide frequency range including microwave frequencies. Analogous formulas also hold for the magnetic permeability with permittivity replaced by permeability wherever it appears in the proposed model.
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Keywords:
- effective permittivity /
- homogenization /
- shielding effectiveness /
- fiber-reinforced composite materials
[1] Liang J J, Huang Y, Zhang F, Li N, Ma Y F, Li F F, Chen Y S 2014 Chin. Phys. B 23 088802
[2] Cordill B D, Seguin S A, Ewing M S 2013 IEEE Trans. Instrum. Meas. 62 743
[3] He H H, Wu M Z, Zhao Z S 1999 Acta Phys. Sin. 48 138 (in Chinese) [何华辉, 吴明忠, 赵振声 1999 48 138]
[4] Holloway C L, Sarto M S, Johansson M 2005 IEEE Trans. Electromagn. Compat. 47 833
[5] Zang Y Z, He M X, Gu J Q, Tian Z, Han J G 2012 Chin. Phys. B 21 117802
[6] Waki H, Igarashi H, Honma T 2005 IEEE Trans. Magn. 41 1520
[7] He Y F, Gong R Z, Wang X, Zhao Q 2008 Acta Phys. Sin. 57 5261 (in Chinese) [何燕飞, 龚荣洲, 王鲜, 赵强 2008 57 5261]
[8] Ding S J, Ge D B, Shen N 2010 Acta Phys. Sin. 59 944 (in Chinese) [丁世敬, 葛德彪, 申宁 2010 59 944]
[9] Preault V, Corcolle R, Daniel L, Pichon L 2013 IEEE Trans. Electromagn. Compat. 55 1178
[10] Wasselynck G, Trichet D, Ramdane B, Fouldagar J 2010 IEEE Trans. Magn. 46 3277
[11] Shen X Q, Liu H B, Wang Z, Qian X Y, Jing M X, Yang X C 2014 Chin. Phys. B 23 078101
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[1] Liang J J, Huang Y, Zhang F, Li N, Ma Y F, Li F F, Chen Y S 2014 Chin. Phys. B 23 088802
[2] Cordill B D, Seguin S A, Ewing M S 2013 IEEE Trans. Instrum. Meas. 62 743
[3] He H H, Wu M Z, Zhao Z S 1999 Acta Phys. Sin. 48 138 (in Chinese) [何华辉, 吴明忠, 赵振声 1999 48 138]
[4] Holloway C L, Sarto M S, Johansson M 2005 IEEE Trans. Electromagn. Compat. 47 833
[5] Zang Y Z, He M X, Gu J Q, Tian Z, Han J G 2012 Chin. Phys. B 21 117802
[6] Waki H, Igarashi H, Honma T 2005 IEEE Trans. Magn. 41 1520
[7] He Y F, Gong R Z, Wang X, Zhao Q 2008 Acta Phys. Sin. 57 5261 (in Chinese) [何燕飞, 龚荣洲, 王鲜, 赵强 2008 57 5261]
[8] Ding S J, Ge D B, Shen N 2010 Acta Phys. Sin. 59 944 (in Chinese) [丁世敬, 葛德彪, 申宁 2010 59 944]
[9] Preault V, Corcolle R, Daniel L, Pichon L 2013 IEEE Trans. Electromagn. Compat. 55 1178
[10] Wasselynck G, Trichet D, Ramdane B, Fouldagar J 2010 IEEE Trans. Magn. 46 3277
[11] Shen X Q, Liu H B, Wang Z, Qian X Y, Jing M X, Yang X C 2014 Chin. Phys. B 23 078101
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