Conductivity of a composite containing uniformly oriented penny-shaped cracks or perfectly conducting discs

We consider the problem of determining the effective conductivity of a comp osite material consisting of parallel discs embedded in an isotropic matrix . A method of multipole expansion is used for computing the conductivity fo r the cases of perfectly conducting discs and non-conducting discs or penny -shaped cracks. Both the cases of periodic and random arrangements of discs or cracks are considered. It is shown that, in general, the conductivity i s quite sensitive to the details of the arrangement of the discs. The resul ts of computations are compared with those obtained using an effective-medi um approximation and with a bound on conductivity.