EFFECTIVE CONDUCTIVITY IN A TWO-PHASE MATERIAL WITH GENERALIZED CHEQUER-BOARD GEOMETRY

In this paper an exact analytical solution of effective conductivity in a two-phase material with the generalized chequer-board geometry is obtained. They are
In(σ_e/σ₂)=In(R+s²/R+1),
Where
R=s(1+ s²)2+ε(ηs² -1)+ s² (s²-1)T(ε,η)/s(1+ s)² ε(1-η)-(s-1)T(ε,η)
And T(ε,η)=Σ H(n)sinh√λ_na(1-η)tan(√λ_nbε)/h sinh(√λ_na ) tan (√λ_nb)
Some calculated results for a=b, n=l and s=50, 7.14 are also shown.