In plane stiffness of multifunctional hierarchical honeycombs with negative Poisson's ratio sub-structures

Compared with triangular, square and Kagome honeycombs, hexagonal honeycomb has superior heat dissipation capabilities, but its lower in-plane stiffness hinders its multifunctional applications. Regarding this problem, in this paper we propose a multifunctional hierarchical honeycomb (MHH) with negative Poisson's ratio (NPR) sub-structures. This MHH is constructed by replacing the solid cell walls of the original regular hexagonal honeycomb (ORHH) with two kinds of equal mass NPR honeycombs, the anisotropic re-entrant honeycomb or the isotropic chiral honeycomb. Based on the Euler beam theory, formulas for the Young's moduli of these two kinds of MHH structures are derived. Results show that by appropriately adjusting the geometrical parameters both the re-entrant honeycomb (when the cell-wall thickness-to-length ratio of the ORHH is less than 0.045) and the chiral honeycomb (when the cell-wall thickness-to-length ratio of the ORHH is less than 0.75) can greatly tune the in-plane stiffness of the MHH structure. The presented theory could thus be used in designing new tailorable hierarchical honeycomb structures for multifunctional applications.