Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4617305 | Journal of Mathematical Analysis and Applications | 2012 | 27 Pages |
Homogenized laws for sequences of high-contrast two-phase non-symmetric conductivities perturbed by a parameter hh are derived in two and three dimensions. The parameter hh characterizes the antisymmetric part of the conductivity for an idealized model of a conductor in the presence of a magnetic field. In dimension two an extension of the Dykhne transformation to non-periodic high conductivities permits to prove that the homogenized conductivity depends on hh through some homogenized matrix-valued function obtained in the absence of a magnetic field. This result is improved in the periodic framework thanks to an alternative approach, and illustrated by a cross-like thin structure. Using other tools, a fiber-reinforced medium in dimension three provides a quite different homogenized conductivity.