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

Abstract

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.

Novel structure with negative Poisson’s ratio and enhanced Young’s modulus

“…In a similar manner as in classical re-entrant configurations [22,23], the increase of relative density a provides an significant increased contribution of the in-plane stiffness ratio value E=E s , while the in-plane Poisson's ratio v decrease little. It is worth note that with a increase the enhancement of Young's modulus decrease.…”

“…Using a similar method given in [22], linear elastic FE models has been created to determine the in-plane properties of the new structure. The ABAQUS commercial package has been used to perform these analyses.…”

“…Combining all three mechanisms of flexing, hinging and stretching, Masters and Evans developed a general model for predicting the in-plane properties of honeycombs [19]. Grima et al [22] modified Masters' analytical formulas in 2011 by considering the realistic thickness-to-length ratio of the re-entrant cell wall. Based on a strain energy technique pioneered by Choi and Lakes [11], Bezazi et al calculated the in-plane Poisson's ratio and Young's modulus of a new centersymmetric honeycomb configuration under uniaxial loading by taking into account manufacturing constraints [23].…”

Geometric effects of sustainable auxetic structures integrating the particle swarm optimization and finite element method

“…The next document reporting the evidence of an auxetic material was found 38 years later by Gibson 3 . In 1987, Lakes made the first discovery about the negative effect of Poisson's ratio designing a polyurethane foam (PU) with reentrant structures, which was named by anti-rubber, auxetic or dilational 4 . In recent years, the studies related to auxetic structures were mainly focused on the estimation of effective properties as a function of geometric dimensions 5 , density variations 6 , electromagnetic 7 , acoustic and mechanical properties 8,9 , and the ability to absorb vibrations 10 .…”

On the mechanical properties of centro‐symmetric honeycombs with T‐shaped joints

“…Another highly realistic model was also suggested by Evans et al where, in addition to the flexure mode of deformation, the honeycombs were also permitted to deform through stretching of the ligaments and a hinging‐type mechanism which involves changes in angle between the ligaments . This model was more recently extended by Grima et al who argued that, in the vicinity of the joints, there are only negligible deformation with the result that the real length of the ribs which is actually deforming is shorter than the length of the rib one normally measures and therefore, one should consider the deformation of an effective length rather than the actual length. Such multi‐mode models are particularly useful in geometries where the contribution of these deformation mechanisms (i.e.…”