The conductivity of a sheet perforated with square holes

Abstract

Homogenization of a square array of square holes is a longstanding problem which does not admit an analytical solution. A number of approximate solutions exist with a broad range of applications, but so far their accuracy was not properly assessed. In this paper two phenomenological models for the effective conductivity of the two-dimensional square array of square holes, based on the Padé approximants of order [3/1] and [2/2], are represented. The models are validated by comparison with numerical simulations, their accuracy and applicability are assessed. We find that they are consistently much more accurate than existing analytical models.