Generalized Chessboard Structures Whose Effective Conductivities Are Integer Valued

Abstract

We consider generalized chessboard structures where the local conductivity takes two values 𝑎 and 𝑏 . All integer combinations of 𝑎 and 𝑏 which make the components of effective conductivity matrix integer valued are found. Moreover, we discuss the problem of estimating the effective conductivity matrix by using the finite-element method.