  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 local damage during impact events. Here we propose
the use of an architected structure composed of hollow truncated cone unit
cells that exhibit structural recovery in place of foams or honeycomb
structures. These structures printed with a viscoelastic material rely on
buckling of their sidewalls to dissipate energy without permanent damage. We
explore the mechanical response of these conical unit cells in terms of their
buckling strength and post-buckling stability condition 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.
