Abstract
We calculate the effective conductivity of a two-phase composite with a periodic array of inhomogeneities. The shape of the inhomogeneities is assumed to be a periodic E-inclusion. The effective conductivity is expressed in terms of the volume fraction of the inhomogeneities and a matrix, which characterizes the shape of the periodic E-inclusion. This solution is rigorous, closed-form, and applicable to situations that the conductivity of the inhomogeneities is singular, i.e., zero or infinite. Further, when the periodic E-inclusion degenerates to a periodic array of slits with vanishing volume fraction, we give explicit solutions to local fields and effective conductivity of the composite with singular inhomogeneities.
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