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

Mohamed Camar-Eddine (1) , Laurent Pater (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

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 [M. Briane and L. Pater. Homogenization of high-contrast two-phase conductivities perturbed by a magnetic field. Comparison between dimension two and dimension three. J. Math. Anal. Appl., 393 (2) (2012), 563 -589] to the case of periodic and non periodic composites with more general transversal geometries.

Mots clés: Homogenization; High-contrast conductivity; Strong field; Two-phase composites; Columnar structures

Domaines: Equations aux dérivées partielles [math.AP]

Mohamed Camar-Eddine, Laurent Pater. Homogenization of high-contrast and non symmetric conductivities for non periodic columnar structures. Networks and Heterogeneous Media, 2013, 8 (4), pp.913-941. ⟨10.3934/nhm.2013.8.913⟩. ⟨hal-00795608v2⟩