Effective properties of some new self-similar structures

Abstract

We consider a self-similar structure of chessboard type with infinitely many micro-scales where the conductivity is locally anisotropic. The effective properties are found by using Γ-convergence techniques. Even though the effective conductivity matrix coincide with that of the standard chessboard structure in the isotropic case, we show that this is generally not the case. Our results are used to construct sequences of two-component material-structures, whose effective conductivities are described by the well-known arithmetic-geometric mean introduced by Legendre and Gauss.

Keywords:

• effective properties; reiterated homogenization; self-similar structures