In this paper we study the magneto-resistance, i.e. the second-order term of
the resistivity perturbed by a low magnetic field, of a three-dimensional
composite material. Extending the two-dimensional periodic framework of [4], it
is proved through a H-convergence approach that the dissipation energy induced
by the effective magneto-resistance is greater or equal to the average of the
dissipation energy induced by the magneto-resistance in each phase of the
composite. This inequality validates for a composite material the Kohler law
which is known for a homogeneous conductor. The case of equality is shown to be
very sensitive to the magnetic fi eld orientation. We illustrate the result
with layered and columnar periodic structures.Comment: 28 page