Homogenization of linearly elastic honeycombs

Abstract

A continuum model for the in-plane deformations of cellular materials with honeycomb texture is derived by using the tools of homogenization theory via Γ-convergence. It is shown that the effective medium does not develop couple stresses, although it exhibits some mild trait of polarity. General stress–strain relations and the yield domains for various levels of the applied body couples are deduced. The paper is a refinement of a previous one based on a less rich microscopic kinematics, but the analysis confirms most of those results.