Homogenization of woven materials

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