EXACT RESULTS FOR THE MACROSCOPIC CONDUCTIVITY TENSOR OF A TWO-CONSTITUENT COMPOSITE WITH A 2D COLUMNAR MICROSTRUCTURE

摘要

In a two-dimensional (2D) or columnar microstructure, the interface between different constituents is always parallel to a fixed direction, which we take to be the x-axis - see Fig. 1. When there are only two constituents, with conductivity tensors (σ~((1)), σ~((2)), the macroscopic conductivity tensor of such a columnar composite can be found by first solving the following 2D conductivity problem.