Estimating the Vigdergauz constants for regular hexagonal honeycombs

In this paper we propose a new model for estimating the effective properties of regular hexagonal honeycombs. This model yields some new simple formulae which, in contrast to previous attempts, match the general invariant relations found by Vigdergauz in 1999. By comparing with numerical results, we also find some improved (but still simple) formulae which enable us to estimate the effective properties with an accuracy better than 1%, even for high density honeycombs.