The purpose of this paper is to provide simple analytical homogenization methods for composite materials containing a metallic wire grid. Estimating their effective electrical properties facilitates the numerical simulation of composite structures for shielding applications in the automotive industry. The presented methods are based on surface impedance approaches and effective media theory. The obtained results show that the shielding properties of the described wire grid composites can be accurately estimated and bounded, using the proposed theories in the low frequency range. The frequency limits vary according to the studied sample. For the presented materials, the validity of the results is shown to be up to a few megahertz. The experimental validation is done by measuring the shielding effectiveness of composite samples using a near-field test bench.
2. Senghor, F. D., G. Wasselynck, H. K. Bui, S. Branchu, D. Trichet, and G. Berthiau, "Electrical conductivity tensor modeling of stratified woven-fabric carbon fiber reinforced polymer composite materials," IEEE Transactions on Magnetics, Vol. 53, 1-4, Jun. 2017.
3. Sutthaweekul, R., A. M. J. Marindra, and G. Y. Tian, "Study of microwave responses on layered woven CFRP composites," 2017 9th International Conference on Information Technology and Electrical Engineering (ICITEE), 1-5, Oct. 2017.
4. Al Achkar, G., L. Pichon, L. Daniel, and N. Benjelloun, "Effective electromagnetic properties of woven fiber composites for shielding applications," IEEE Transactions on Electromagnetic Compatibility, Vol. 62, No. 4, 1082-1089, Aug. 2020.
5. Lovat, G., "Near-field shielding effectiveness of 1-D periodic planar screens with 2-D near-field sources," IEEE Transactions on Electromagnetic Compatibility, Vol. 51, No. 3, 708-719, 2009.
6. Araneo, R., G. Lovat, and S. Celozzi, "Shielding effectiveness of periodic screens against finite high-impedance near-field sources," IEEE Transactions on Electromagnetic Compatibility, Vol. 53, No. 3, 706-716, 2011.
7. Benhamou, S., M. Hamouni, and S. Khaldi, "Theoretical approach of electromagnetic shielding of multilayer conductive sheets," Progress In Electromagnetics Research M, Vol. 41, 167-175, 2015.
8. Casey, K. F., "Electromagnetic shielding behavior of wire-mesh screens," IEEE Transactions on Electromagnetic Compatibility, Vol. 30, 298-306, Aug. 1988.
9. Sarto, M. S. and C. L. Holloway, "Effective boundary conditions for the time-domain analysis of the EMC performances of fiber composites," 1999 IEEE International Symposium on Electromagnetic Compatability. Symposium Record (Cat. No. 99CH36261), Vol. 1, 462-467, Aug. 1999.
10. Sarto, M. S., S. Greco, and A. Tamburrano, "Shielding effectiveness of protective metallic wire meshes: EM modeling and validation," IEEE Transactions on Electromagnetic Compatibility, Vol. 56, 615-621, Jun. 2014.
11. Liang, R., W. Cheng, H. Xiao, M. Shi, Z. Tang, and N. Wang, "A calculating method for the electromagnetic shielding effectiveness of metal fiber blended fabric," Textile Research Journal, Vol. 88, No. 9, 973-986, 2018.
12. Liu, Y. and J. Tan, "Frequency dependent model of sheet resistance and effect analysis on shielding effectiveness of transparent conductive mesh coatings," Progress In Electromagnetics Research, Vol. 140, 353-368, 2013.
13. Hashin, Z. and S. Shtrikman, "A variational approach to the theory of the effective magnetic permeability of multiphase materials," Journal of Applied Physics, Vol. 33, 3125-3131, Oct. 1962.
14. Hashin, Z. and S. Shtrikman, "A variational approach to the theory of the elastic behaviour of multiphase materials," Journal of the Mechanics and Physics of Solids, Vol. 11, No. 2, 127-140, 1963.
15. Sihvola, A., Electromagnetic Mixing Formulas and Applications, Electromagnetics and Radar Series, Institution of Electrical Engineers, 1999.
16. Bal, K. and V. Kothari, "Permittivity of woven fabrics: A comparison of dielectric formulas for air-fiber mixture," IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 17, 881-889, Jun. 2010.
17. Holloway, C., M. Sarto, and M. Johansson, "Analyzing carbon-fiber composite materials with equivalent-layer models," IEEE Transactions on Electromagnetic Compatibility, Vol. 47, 833-844, Nov. 2005.
18. Koledintseva, M. Y., R. E. DuBroff, and R. W. Schwartz, "A Maxwell Garnett model for dielectric mixtures containing conducting particles at optical frequencies," Progress In Electromagnetics Research, Vol. 63, 223-242, 2006.
19. Andrieu, G., J. Panh, A. Reineix, P. Pelissou, C. Girard, X. Romeuf, and D. Schmitt, "Homogenization of composite panels from a near-field magnetic shielding effectiveness measurement," IEEE Transactions on Electromagnetic Compatibility, Vol. 54, 700-703, Jun. 2012.
20. Greco, S., A. Tamburrano, A. D’Aloia, R. Mufatti, and M. S. Sarto, "Shielding effectiveness properties of carbon-fiber reinforced composite for HIRF applications," International Symposium on Electromagnetic Compatibility — EMC EUROPE, 1-6, Sep. 2012.
21. Yatsenko, V. V., S. A. Tretyakov, S. I. Maslovski, and A. A. Sochava, "Higher order impedance boundary conditions for sparse wire grids," IEEE Transactions on Antennas and Propagation, Vol. 48, 720-727, May 2000.
22. Awan, Z. A., "Surface impedance properties of a wire grid embedded in a chiral medium," International Journal of Microwave and Wireless Technologies, Vol. 12, No. 1, 58-65, 2020.
23. Karkkainen, K. K., A. H. Sihvola, and K. I. Nikoskinen, "Effective permittivity of mixtures: Numerical validation by the FDTD method," IEEE Transactions on Geoscience and Remote Sensing, Vol. 38, 1303-1308, May 2000.
24. Robinson, M. P., T. M. Benson, C. Christopoulos, J. F. Dawson, M. D. Ganley, A. C. Marvin, S. J. Porter, and D. W. P. Thomas, "Analytical formulation for the shielding effectiveness of enclosures with apertures," IEEE Transactions on Electromagnetic Compatibility, Vol. 40, No. 3, 240-248, 1998.
25. Fang, C.-H., S. Zheng, H. Tan, D. Xie, and Q. Zhang, "Shielding effectiveness measurements on enclosures with various apertures by both mode-tuned reverberation chamber and GTEM cell methodologies," Progress In Electromagnetics Research B, Vol. 2, 103-114, 2008.
26. Harid, V., M. Golkowski, S. D. Gedney, M. B. Cohen, S. K. Patch, R. A. L. Rorrer, C. M. Renick, J. Bittle, N. M. Opalinski, and H. Y. Kim, "Magnetic field penetration into a metal enclosure using an ELF/VLF loop antenna," IEEE Transactions on Electromagnetic Compatibility, 1-12, 2019.
27. Benyoubi, F., L. Pichon, M. Bensetti, Y. Le Bihan, and M. Feliachi, "An efficient method for modeling the magnetic field emissions of power electronic equipment from magnetic near field measurements," IEEE Transactions on Electromagnetic Compatibility, Vol. 59, 609-617, Apr. 2017.
28. Benyoubi, F., M. Feliachi, M. Bensetti, Y. Le Bihan, and L. Pichon, "Fast evaluation of low frequency near field magnetic shielding effectiveness," 2018 IEEE International Symposium on Electromagnetic Compatibility and 2018 IEEE Asia-Pacific Symposium on Electromagnetic Compatibility (EMC/APEMC), 350-354, May 2018.
29. Moser, J. R., "Low-frequency shielding of a circular loop electromagnetic field source," IEEE Transactions on Electromagnetic Compatibility, Vol. 9, 6-18, Mar. 1967.
30. Celozzi, S., R. Araneo, and G. Lovat, Electromagnetic Shielding, John Wiley & Sons, Ltd., 2008.
31. Geuzaine, C. and J.-F. Remacle, "GMSH: A 3-D finite element mesh generator with built-in preand post-processing facilities," International Journal for Numerical Methods in Engineering, Vol. 79, 1309-1331, 2009.
32. Dular, P., C. Geuzaine, F. Henrotte, and W. Legros, "A general environment for the treatment of discrete problems and its application to the finite element method," IEEE Transactions on Magnetics, Vol. 34, 3395-3398, Sept. 1998.