An Improved Analytical Model for the Elastic Constants of Auxetic and Conventional Hexagonal Honeycombs

Cellular solids, in particular hexagonal honeycombs have been the subject of numerous studies in the last decades in view of their extensive use in many applications. In particular, there have been various studies aimed at expressing the mechanical properties of honeycombs in terms of the geometrical parameters used to describe the structure of such honeycombs. Despite improvements over the first established model, finite element simulations performed in this work on honeycombs having ribs with a realistic thickness-to-length ratio suggest that the mechanical properties for such systems differ from those predicted by current models, sometimes to a very significant extent. In view of this, we analyse in detail the deformed structures in an attempt to gain insight into how and the extent to which the shape of the ligaments, in particular its thickness and mode of connection affects deformation in conventional and re-entrant hexagonal honeycombs. Based on these observations, we propose a modified version of the previous analytical models that take into consideration the finite thickness of the ligaments.