Stability of an elastic honeycomb under out-of-plane compression

The present study focuses on the nonlinear axial response of an elastic honeycomb and the associated instabilities that govern it. Simulations on numerical models with finite size domains reveal that the compressive behavior of elastic honeycombs is a product of a cascade of bifurcations with distinct characteristics. Stability analysis on periodic unit cells and finite domain structures shows that the first bifurcation corresponds to local plate buckling with a single wave formed across the honeycomb height. This is followed by a series of mode-jumping bifurcations that alter the wavelength of the buckled cell walls across the domain with, however, minimal effect on the macroscopic response. At increased compression, localization initiates in the form of folding at a boundary wall, leading to a continuously decreasing tangent stiffness which terminates at a global limit load. At this point, all exterior plates have localized, and the distortional buckling mode propagates in the interior cells. We further examine and quantify the effect of higher volume fractions, different domain size and shapes, and material nonlinearity on each critical stress and associated deformation mode.