The effective conductivity of a periodic lattice of circular inclusions
  We determine the effective conductivity of a two-dimensional composite consisting of a doubly periodic array of identical circular cylinders within a homogeneous matrix. We obtain an exact analytic expression for the effective conductivity tensor as well as its expansion in terms of volume fraction of the cylinders. Results are illustrated by examples. 
Yuri A. Godin
cond-mat.mtrl-sci math-ph math.AP math.MP physics.class-ph