Irregular and Regular Honeycomb Lattice Structures: Effective Properties and Design Perspectives

Abstract

A unified approach to determine the effective elastic properties of irregular and regular honeycomb (Hc) lattice structures is presented. A micromechanics model of a lattice, based on the fundamental periodic element, is developed using Castigliano’s second theorem to obtain a homogenized strain energy density function that yields all elastic properties of the lattice. The lattice geometry, comprising uniform slender beam elements, is specified by six lattice parameters for irregular lattices and four lattice parameters for regular lattices. These parameters generate Hc or re-entrant honeycomb (RHc) structures with different symmetry properties, which can cater to different design requirements. A comprehensive validation, including comparison with available analytical and full finite element (FE) results for different geometries and dimensions, confirms the accuracy of the proposed approach. The influence of the geometric parameters on the effective lattice properties is clearly revealed, which leads to some novel design insights. The existence of the continuous and accidental L4 symmetry axis in tuned Hc and RHc lattices (including irregular ones) is brought out for the first time in this analysis. Interestingly, it is observed that high auxeticity coincides with low shear modulus, contrary to the existing postulate of high auxeticity that implies high shear stiffness. It is also shown that auxeticity is a directional property in RHc lattice structures.