volume | PIER Journals

Abstract

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.

1. El Feddi, M., Z. Ren, A. Razek, and A. Bossavit, "Homogenization technique for Maxwell equations in periodic structures," IEEE Transactions on Magnetics, Vol. 33, 1382-1385, Mar. 1997.
doi:10.1109/20.582514 Google Scholar

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.
doi:10.1109/TMAG.2017.2660529 Google Scholar

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. Google Scholar

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.
doi:10.1109/TEMC.2019.2931764 Google Scholar

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.
doi:10.1109/TEMC.2009.2022273 Google Scholar

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.
doi:10.1109/TEMC.2010.2081367 Google Scholar

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.
doi:10.2528/PIERM15020101 Google Scholar

8. Casey, K. F., "Electromagnetic shielding behavior of wire-mesh screens," IEEE Transactions on Electromagnetic Compatibility, Vol. 30, 298-306, Aug. 1988.
doi:10.1109/15.3309 Google Scholar

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.
doi:10.1109/ISEMC.1999.812948 Google Scholar

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.
doi:10.1109/TEMC.2013.2292715 Google Scholar

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.
doi:10.1177/0040517517693980 Google Scholar

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.
doi:10.2528/PIER13050312 Google Scholar

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. Google Scholar

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.
doi:10.1016/0022-5096(63)90060-7 Google Scholar

15. Sihvola, A., Electromagnetic Mixing Formulas and Applications, Electromagnetics and Radar Series, 1999.
doi:10.1049/PBEW047E

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.
doi:10.1109/TDEI.2010.5492262 Google Scholar

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. Google Scholar

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.
doi:10.2528/PIER06052601 Google Scholar

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.
doi:10.1109/TEMC.2012.2186455 Google Scholar

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. Google Scholar

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.
doi:10.1109/8.855490 Google Scholar

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.
doi:10.1017/S1759078719000953 Google Scholar

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.
doi:10.1109/36.843023 Google Scholar

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.
doi:10.1109/15.709422 Google Scholar

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. Google Scholar

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. Google Scholar

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.
doi:10.1109/TEMC.2016.2643167 Google Scholar

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.
doi:10.1109/ISEMC.2018.8393796 Google Scholar

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.
doi:10.1109/TEMC.1967.4307447 Google Scholar

30. Celozzi, S., R. Araneo, and G. Lovat, Electromagnetic Shielding, John Wiley & Sons, Ltd., 2008.
doi:10.1002/9780470268483

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.
doi:10.1002/nme.2579 Google Scholar

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.
doi:10.1109/20.717799 Google Scholar

Dr. Ghida Al Achkar

Dr. Lionel Pichon

Dr. Mohamed Bensetti

Dr. Laurent Daniel