The in-plane elastic-plastic response of hierarchical honeycombs with sandwich walls

We examine both theoretically and numerically the in-plane elastic-plastic response of hierarchical honeycombs composed of sandwich-structured cell walls. An analytical model was developed to predict the effective collapse stress of sandwich-structured honeycombs (SSHC) under in-plane uniaxial, biaxial and shear loading. The collapse of SSHCs was shown to occur by three competing mechanisms: core shear, face yielding and elastic buckling. Collapse mechanism maps were constructed showing dominance of core shear and face yielding collapse for metallic SSHCs with practical design parameters, while elastic buckling was only observed for polymeric SSHCs. The analytical predictions of the collapse load and dominant mechanism were found in good agreement with those obtained from detailed finite element calculations for a range of geometrical and material parameters. Moreover, the analytical model was used to determine optimal architectural parameters that maximize the collapse stress for a range of relative densities, concluding that slender sandwich walls with relatively thick faces yield optimal performance for SSHCs with weak cores and low relative densities (<10 %). Lastly, it was found that SSHCs attain higher collapse stresses by up to 600 % for certain designs compared to conventional monolithic honeycombs of equal relative density.