Homogenization of woven materials

In English The effective electric and magnetic material properties of a complex (twocomponent)
mixture are addressed. The mixture is periodic in two directions
and has a finite thickness in the third direction. Specifically,the explicit problem
of finding the effective electric parameters for slab that has been reinforced
by a layer (or several layers) of glass fiber is investigated. The homogenization
problem is solved by a series expansion (multiple-scale technique),and
the numerical solution of the two-dimensional vector-valued problem is found
by a FEM formulation. The FEM problem is non-standard due to the periodic
boundary conditions of the problem. Several numerical computations show
that the most important parameter of the effective permittivity is the volume
fraction of the guest material in the host. The reflection and transmission
properties of the homogenized material are also addressed.