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

Mohamed Camar-Eddine; Laurent Pater

doi:10.3934/nhm.2013.8.913

Article Contents

2013, Volume 8, Issue 4: 913-941. Doi: 10.3934/nhm.2013.8.913

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

Mohamed Camar-Eddine^1, and
Laurent Pater^2,

1.
Centre de Mathématiques, I.N.S.A. de Rennes & I.R.M.A.R., Rennes Cedex
2.
I.R.M.A.R., Université de Rennes 1, Rennes Cedex

Received: February 2013

Published: December 2013

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Abstract

In this paper we determine, in dimension three, the effective conductivities of non periodic and 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.

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Mathematics Subject Classification: Primary: 35B27, 35J25; Secondary: 74Q20.

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