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Materials (Basel). 2013 Nov 21;6(11):5367-5381. doi: 10.3390/ma6115367.

Equivalent Electromagnetic Constants for Microwave Application to Composite Materials for the Multi-Scale Problem.

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Toyota Technological Institute, 2-12-1 Hisakata, Tenpaku-ku, Nagoya-city 468-8511, Japan.
Toyota Technological Institute, 2-12-1 Hisakata, Tenpaku-ku, Nagoya-city 468-8511, Japan.
Kojima Press Industry Co. Ltd., 15 Hirokuden, Ukigai-cho, Miyoshi-city 470-0207, Japan.


To connect different scale models in the multi-scale problem of microwave use, equivalent material constants were researched numerically by a three-dimensional electromagnetic field, taking into account eddy current and displacement current. A volume averaged method and a standing wave method were used to introduce the equivalent material constants; water particles and aluminum particles are used as composite materials. Consumed electrical power is used for the evaluation. Water particles have the same equivalent material constants for both methods; the same electrical power is obtained for both the precise model (micro-model) and the homogeneous model (macro-model). However, aluminum particles have dissimilar equivalent material constants for both methods; different electric power is obtained for both models. The varying electromagnetic phenomena are derived from the expression of eddy current. For small electrical conductivity such as water, the macro-current which flows in the macro-model and the micro-current which flows in the micro-model express the same electromagnetic phenomena. However, for large electrical conductivity such as aluminum, the macro-current and micro-current express different electromagnetic phenomena. The eddy current which is observed in the micro-model is not expressed by the macro-model. Therefore, the equivalent material constant derived from the volume averaged method and the standing wave method is applicable to water with a small electrical conductivity, although not applicable to aluminum with a large electrical conductivity.


eddy current; electrical conductivity; equivalent material constant; multi-scale

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