  In this paper, we propose a novel design and fabrication strategy to produce
architected core structures for use as the core in composite sandwich
structures. A traditional foam core or honeycomb structure is lightweight and
stiff, but susceptible to permanent deformation when subjected to excessive
loading. Here we propose the use of an architected structure composed of arrays
of hollow truncated cone unit cells that dissipate energy and exhibit
structural recovery. These structures printed with a viscoelastic material rely
on buckling of their sidewalls to dissipate energy and snap-back to prevent
permanent deformation. We explore the mechanical response of these conical unit
cells in terms of their buckling strength and post-buckling stability
condition, and develop design maps for the same, by relating them to
non-dimensional geometric parameters $\alpha$, $\beta$, $\gamma$, where
$\alpha$ represents the slenderness of the curved sidewalls, $\beta$ is the
angle of the sidewall to the base, and $\gamma$ represents the curvature of the
sidewall. A validated finite element model is developed and used to investigate
the effect of these parameters. We see that the peak buckling load is directly
proportional to both $\alpha$ & $\beta$ and is not dependent on $\gamma$ when
the load is normalized by the volume of material in the curved sidewall.
Interestingly, the post-buckling stability is influenced by $\gamma$, or the
initial curvature of the sidewall, where a larger radius of curvature makes the
structure less susceptible to exhibit structural bistability. The structures
presented here are printed using a viscoelastic material, that causes them to
exhibit pseudo-bistability, or a time-delayed recovery. This allows the
structures to buckle and dissipate energy, and then recover to their original
configurations without the need for external stimuli or energy.
