Inverse homogenization with diagonal Padé approximants

The paper formulates inverse homogenization problem as a problem of recovery of Markov function using diagonal Padé approximants. Inverse homogenization or de-homogenization problem is a problem of deriving information about the microgeometry of composite material from its effective properties. The approach is based on reconstruction of the spectral measure in the analytic Stieltjes representation of the effective tensor of two-component composite. This representation relates the n-point correlation functions of the microstructure to the moments of the spectral measure, which contains all information about the microgeometry. The problem of identification of the spectral function from effective measurements in an interval of frequency has a unique solution. The problem is formulated as an optimization problem which results in diagonal Padé approximation and exact formulas for the moments of the measure. The reconstructed spectral function can be used to evaluate geometric parameters of the structure and to compute other effective parameters of the same composite; this gives solution to the problem of coupling of different effective properties of a two-component composite material with random microstructure.