Homogenization of high-contrast and non symmetric conductivities for non periodic columnar structures

In this paper we determine, in dimension three, the effective conductivities of non periodic high-contrast two-phase cylindrical composites, placed in a constant magnetic field, without any assumption on the geometry of their cross sections. Our method, in the spirit of the H-convergence of Murat-Tartar, is based on a compactness result and the cylindrical nature of the microstructure. The homogenized laws we obtain extend those of the periodic fibre-reinforcing case of [17] to the case of periodic and non periodic composites with more general transversal geometries.