Abstract
We derive an expansion of the voltage potential in a composite medium, made of circular conducting inclusions of small diameter $\varepsilon$ embedded in a homogeneous matrix phase, when the inhomogeneities are strongly interacting, i.e., when they are very close or even touching. The asymptotics of the voltage potential depend on the position of the inclusions and on the contrast between the inclusions and matrix conductivities via a polarization tensor. We are especially interested in determining an analytical expression of this tensor in order to study how the terms in the expansion depend on the interinclusion distance, the inclusion size, and the conductivity contrast. We present numerical tests that compare the true voltage potential to our asymptotic formula when the inclusions are treated as a single inhomogeneity and to the asymptotic formula when the inclusions are well separated.