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Bionic and gradient designs offer promising applications in honeycomb structures. The intersection unit of the beetle elytra is extracted as to enhance regular hexagonal honeycomb (RHH), and several bionic honeycombs are proposed. Finite element (FE) modeling approach is verified through formulae and experiments. Curves of force and displacement of bionic honeycombs present two prominent stages under medium- and low-speed impacts in plateau stage, and several bionic honeycombs exhibit a zero or negative Poisson's ratio. The specific energy absorption (SEA) of INT_6, whose crashworthiness is best in bionic honeycombs. A gradient design of INT_6 is implemented to further increase its crashworthiness. Multi-objective optimization design (MOD), which aims to simultaneously increase the SEA and reduce the peak crushing force, is adopted to determine the optimal parameters of each layer of graded INT_6. The SEA of the optimized graded INT_6 increase 142%, and its peak crushing force decrease by 25.4% compared with those of the INT_6. [ABSTRACT FROM AUTHOR]

• Novel horsetail bio-honeycombs (HBHs) are proposed based on horsetail stems. • A theoretical model of HBHs is established to predict their average impact force. • The membrane energy for novel 5-panel and 7-panel corner elements are derived. • Three deformation modes are observed based on the thickness-length ratio of HBHs. • The HBHs exhibit significant crashworthiness advantages with same relative density. Inspired by the ingenious cross-sectional structure of horsetail stems, a group of novel horsetail bio-honeycombs (HBHs) are firstly proposed to pursuit a superior impact resistance performance. The out-of-plane impact resistance characteristics and mechanical properties of the proposed HBHs are investigated by means of test, theoretical analysis, and finite element (FE) analysis. In the process of deriving the theoretical model of HBHs, the novel 5-panel and 7-panel membrane energy dissipation corner elements are firstly proposed and reasonable theoretical solutions for them are obtained. Theoretical results suggest that the errors between numerical and theoretical results for the majority of the HBHs are within 7 %. In addition, the studies indicate that the HBHs outperform the circular honeycomb (CH) in terms of crashworthiness while ensuring that their relative densities are the same. The complex proportional assessment method is utilized to evaluate the crashworthiness of HBH _n_6_1.5 (n represents the number of ribs, 6 represents the size of the outer diameter, and 1.5 represents the ratio (ζ) of the outer diameter to the inner diameter) under the same relative density. Furthermore, results suggest that energy absorption and crushing force efficiency of HBH _16_6_1.5 are 31.31 % and 25.54 % higher than those of CH, respectively. Subsequently, the influences of geometric parameters, including the ζ and the thickness-to-cell length ratio (TL), on the impact resistance of HBH _16_6_1.5 are investigated thoroughly. The findings show that when the ζ is within 1.2–1.5, the HBHs can exert their maximum potential, in which the inner diameter of HBHs is close to its outer diameter. Also, the findings demonstrate that the HBHs will undergo three distinct deformation modes. When the TL is roughly within 0.0200–0.0267, the deformation of HBHs will be in the transition deformation mode. [Display omitted] [ABSTRACT FROM AUTHOR]

• Novel horsetails bio-honeycombs are proposed by imitating microstructures of horsetails. • The interaction effect between bionic units and regular hexagonal frame can promote EA. • The ratio of cell wall thickness to length determines deformation modes of bio-honeycombs. • A theoretical model is developed to predict the mean force of horsetails bio-honeycombs. The bionic strategy is regarded as a highly effective design approach for honeycomb structures. To improve the crushing resistance of the honeycombs, some novel bio-honeycombs are proposed by introducing the microstructure of horsetail stems into regular hexagonal honeycomb (RH) cells in this study. Two types of developed bio-honeycombs are considered, including MP type and CC type. A circular honeycomb compression test is carried out to validate the finite element (FE) model. Subsequently, FE models of bio-honeycombs are established to investigate their out-of-plane crashworthiness. The results suggest that the introduced bionic units and the RH frame component will produce a significant interaction effect, where more severe plastic deformation will be formed at their intersections and more folding lobes are formed on the cell walls. Furthermore, the effect of geometric parameters on crashworthiness of MP_6 (MP type with six ribs) bio-honeycombs is discussed. It demonstrates that the smaller cell size of bio-honeycomb is beneficial for improving the utilization efficiency of materials. The deformation modes of MP_6 bio-honeycombs are determined by the ratio of cell wall thickness to cell length (t/l), and the global bending occurs when t/l exceeds 0.0625. In addition, a theoretical model for estimating the mean crushing force of MP_6 bio-honeycombs is derived, and the error with the FE results is within 7%, confirming that the theoretical solution is in good agreement with the simulation. [Display omitted] [ABSTRACT FROM AUTHOR]

• Inspired by beetle elytra intersection unit, a series of novel bionic honeycombs were designed. • Several bio-honeycombs exhibit zero or negative Poisson's ratio. • Bio-honeycombs can improve plateau stress and reduce the peak force effectively. A series of novel bionic honeycombs (bio-honeycombs) are proposed by incorporating the microstructure of the beetle elytra intersection unit into the regular hexagonal honeycomb (Hex) cell. To explore the in-plane mechanical properties and energy absorption performance of bio-honeycombs under different impact speeds, finite element (FE) models are established and verified by empirical formulas and current experiments. The results indicate that the bio-honeycombs outperform the Hex in terms of energy absorption capacity, and the nominal stress–strain curves of the bio-honeycombs show two prominent stages (stage Ⅰ and stage Ⅱ) under quasi-static and mid-impact. Bionic units also undergo two evident deformation stages: preliminary collapse and further crushing. The bending and traction of bionic units make more adjacent cells added to the collapse earlier, forming a global crushed trend, leading to an interesting phenomenon that the localized band of bio-honeycombs are always wider than that of Hex. Also, negative Poisson's ratio is observed in stage Ⅱ from several bio-honeycombs under quasi-static and mid-speed due to bionic units' bending and traction in the further crushing stage. Besides, the number and distribution of ribs have a considerable impact on the crashworthiness of bio-honeycombs. Compared with the Hex, the incorporated bionic units reduce the peak crushing force (PCF) while improving the crashworthiness of bio-honeycomb in the case of the same relative density, which provides a promising potential solution to strengthen the energy absorption performance of honeycomb structures. [ABSTRACT FROM AUTHOR]

• The effect of thickness and reinforced strut gradients on the crushing response of RRH is explored. • Two plateau stresses of RRH specimens are derivated theoretically with a relative error of less than 7 %. • Both thickness and catenary gradients inspire a multi-step deformation mode and multi-plateau stress. • Some suitable thickness and catenary gradients are discovered under different impact velocities. Re-entrant honeycombs have demonstrated promising applications in engineering fields attributed to better manufacturability and adaptability. Herein, the reinforced re-entrant honeycombs (RRH) with thickness and reinforced strut gradients are proposed, respectively, and their in-plane energy absorption is investigated through experiment, theoretical analysis, and simulation. Metallic specimens of uniform and graded RRH are manufactured through a step-by-step method. The deformation mode and plateau stress (PS) of these specimens are significantly influenced by both thickness and catenary gradients. Two PSs of RRH specimens are predicted theoretically with a relative error of less than 7.0 %. Subsequently, the deformation mode and energy absorption of uniform and graded RRH, subjected to varying load rates, are investigated thoroughly with a numerical method verified against the experimental data. The results show that both thickness and catenary gradients can inspire multi-step deformation mode and prevent instability deformation. Compared to uniform RRH (U-RRH), the specific energy absorptions (SEA) of thickness gradient (TG)-123 (123 represents that the thicknesses from impact end to fixed end are t 1 , t 2 , t 3) and TG-213 are enhanced by 52.2 % and 49.8 %, respectively, under quasi-static compression, the SEA of TG-132 and TG-123 are raised by 41.6 % and 20.2 %, respectively, under low-velocity impact, and the SEA of strut gradient (SG)-123 is 66.7 % higher than that of U-RRH under high-velocity impact. More significant auxetic deformation does not always mean better energy absorption because there is also an increased tendency of global instability and earlier densification points. This work provides a novel approach to designing high-energy absorption honeycombs with low structural complexity. [ABSTRACT FROM AUTHOR]

Arched structures have increased in importance over the last few years due to their high efficiency in bearing loads. This paper introduces arched ribs to the classical re-entrant honeycomb (RH) as reinforced structures, and then its energy absorption is improved by simultaneously utilizing the reinforced structures and the auxetic deformation of RHs. Herein, the in-plane crashing response of reinforced RHs (RRH) under different impact velocities is investigated with finite element methods verified against the quasi-static compression experiment of 3D-printed RRH specimens. By introducing arched structures, the deformation of RHs becomes more stable and regular, and two plateau stresses are produced in the stress-strain curves of RRHs. Benefiting from the stacking deformation of RRHs and pure compression characteristic of catenary arches, the second plateau stress of all-reinforced RHs (ARH) is 3.8 times higher than the first one. Two plateau stresses of ARHs are derivated theoretically with a relative error of less than 7 %. Furthermore, a parametric study is performed to explore the effect of impact velocities, thicknesses, and the height of arched ribs on the crashing response of RRHs. The present investigation paves a new way toward strengthening the energy absorption of conventional honeycombs. [ABSTRACT FROM AUTHOR]