Additively manufactured self-similar embedded honeycombs with programmable compressive response

Re-entrant honeycombs (RHs) are widely studied auxetic metamaterials, yet their hierarchical enhancement is usually limited by fixed configurations, where the spatial distribution of hierarchical features remains unexplored as a design variable. Here, a binary-encoded self-similar embedded re-entrant honeycomb (SERH) is proposed by introducing selective hierarchical embedding into a staggered RH lattice. Two geometrically compatible cell states, including non-embedded and self-similarly embedded configurations, are defined and spatially regulated through a column-wise binary encoding strategy. The proposed structures are fabricated via additive manufacturing, and an integrated framework combining analytical modeling, finite element simulation, and experiments is established to investigate their mechanical responses. Results demonstrate that the SERH exhibits stable symmetric collapse, distributed plastic deformation, and enhanced energy absorption compared with conventional RHs. It achieves up to 106.9% improvement in specific energy absorption and 750% enhancement in specific stiffness while maintaining tunable auxetic behavior. Furthermore, binary selective embedding enables hierarchical-gradient architectures with programmable collapse sequences and stress-plateau responses, providing a physically interpretable strategy for designing adaptive auxetic metamaterials.