Quasi-static behavior and energy absorption of bidirectional re-entrant cross-star honeycomb with multi-step deformation

Abstract

Auxetic honeycombs with multi-step deformation are critical for energy absorption applications, yet conventional designs often suffer from single-stage stress plateaus and unstable collapse modes. To address these limitations, this study proposes a novel bidirectional re-entrant cross-star honeycomb (BRSH) through a deformation coordination strategy that integrates reinforcement ribs and internal cross-star embedding. The BRSH replaces concave corners of traditional star-shaped units with linear ribs, introduces transverse inclined ribs, and embeds a cross-star substructure to enable synergistic multi-step deformation. Quasi-static compression tests and finite element (FE) simulations demonstrate that the BRSH exhibits three distinct stress plateaus without initial peak stress, achieving a more than 90 % enhancement in specific energy absorption (SEA) compared to other conventional auxetic honeycombs. Theoretical models based on plastic hinge energy dissipation accurately predict the plateau stresses, revealing a 362.6 % increase in the third plateau stress over the first stage. Furthermore, parametric studies highlight the tunability of the BRSH: adjusting geometric parameters (e.g., β, γ, l₄) allows switching between one-, two-, or three-step deformation modes, while the Poisson's ratio can be tailored from −0.09 to −0.80. The novelty of this work lies in the innovative structural design of the metamaterial and its resulting distinctive mechanical response. And these results establish the BRSH as a high-performance energy absorber with design flexibility, offering new avenues for lightweight and multi-level protective structures in aerospace and automotive engineering.