Abstract
The main purpose of this article is to study the two-scale behavior of the electromagnetic field in 3D in and near composite material. For this, time-harmonic Maxwell equations, for a conducting two-phase composite and the air above, are considered. Technique of two-scale convergence is used to obtain the homogenized problem.
Highlights
We are interested in the time-harmonic Maxwell equations in and near a composite material with boundary conditions modeling electromagnetic field radiated by an electromagnetic pulse (EMP)
It may be generated by a natural occurrence such like a lightning strike, meteoric EMP, EMP caused by geomagnetic Storm or nuclear EMP
We study the electromagnetic pulse caused by this lightning strike
Summary
We are interested in the time-harmonic Maxwell equations in and near a composite material with boundary conditions modeling electromagnetic field radiated by an electromagnetic pulse (EMP). In aircrafts, composite materials consisting of a resin enclosing carbon fibers have significant advantages in terms of weight gain and fuel saving They are much less electrical conductors with loss of the Faraday effect: 100 to 1000 times lower than aluminum. N. Wellander homogenized linear and non-linear Maxwell equations with perfect conducting boundary conditions using two-scale convergence in [26] and [27]. Shelukhin perform twoscale homogenization time-harmonic Maxwell equations for a periodical structure in [5] They calculate the effective dielectric ε and effective electric conductivity σ. The last Section is devoted to the homogenization of the problems for electric field using the two-scale convergence concept
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