Conductivity of composites with multiple polygonal aggregates, theoretical estimates and numerical solutions from polarization series

In this paper, we estimates the effective conductivity of heterogeneous materials constituted aggregates of different polygonal shapes mixed with a matrix material. The problem is considered in the context of periodic homogenization theory. The local problem is formulated using the Lippmann-Schwinger equation of polarization with optimal operator norm. The equation can be used to derive a Fast Fourier Transform (FFT) based iteration scheme and theoretical estimates of the overall properties. When applied to microstructure with polygonal inclusion, the results show a very good agreement between those approaches.