Abstract
This paper provides new bounds on the effective properties in dimension two of multiphase composites with isotropic phases having nonsymmetric conductivities. This is relevant to classical strong field magneto-transport in heterogeneous conductors with columnar microstructure, with a magnetic field in the direction of the columns. On the one hand, a polygon-like G-closure for multiphase composites without prescribed volume fractions is derived for isotropic effective resistivities. On the other hand, the G-closure of the possible average currents associated with a given applied electric field is found for anisotropic multiphase composites with prescribed volume fractions. This extends the G-closure result obtained by Rai˘tum and Tartar for symmetric conductivities.
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