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Homogenization of high-contrast and non symmetric conductivities for non periodic columnar structures. (English) Zbl 1304.35060

Summary: 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 [M. Briane and L. Pater, J. Math. Anal. Appl. 393, No. 2, 563–589 (2012; Zbl 1276.35021)] to the case of periodic and non periodic composites with more general transversal geometries.

MSC:

35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
35J25 Boundary value problems for second-order elliptic equations
74Q20 Bounds on effective properties in solid mechanics

Citations:

Zbl 1276.35021
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