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• 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]

• The novel helical layered square honeycombs exhibit higher strength (∼176 %) and specific energy absorption (∼502 %) than regular square honeycomb. • The quasi-static compressive behaviors of helical-layered and regular square honeycombs are compared. • The deformation modes of helical-layered square honeycombs are dominated by the relative density and the number of helical layer. • The mechanical properties and energy absorption capacity improved by increasing the number of helical layer. • The failure mechanisms of helical-layered square honeycombs are dominated by layer cracking. Bionics shape design of cellular structures has the potential advantage of improving their both mechanical properties and energy absorption capabilities to the conventional honeycomb structures. In this article, inspired by square porous wood and DNA double helix, we demonstrate the creation of the novel helical layered square honeycombs (HLSHs) that simultaneously exhibit high strength and excellent energy absorption capacity. In-plane compression experiments and finite element simulations revealed that helical structure can effectively strengthen every unit cell to resist local stress concentration which always leads to rapid strain localization and finally followed by catastrophic collapse. Furthermore, the stiffness, strength and energy absorption capability can be continuously improved by increasing the number of helical layers. More specifically, the HLSH-4L (4 layers) exhibits higher collapse stress (∼176 %) and specific absorption energy (∼502 %) compared with that of regular square honeycomb (RESH). The investigation of deformation and failure behavior show that the helical structure can supply high cell-buckling resistance and facilitate the "X" shape deformation band. Besides, the helical structure also caused the transition of failure mechanisms from printing fibers tearing in RESH to layer cracking in HLSHs. This study can present insight into the design of lighter and stronger honeycomb. [ABSTRACT FROM AUTHOR]

• A novel bi-material multistable auxetic honeycomb (BMAH) with reusable and enhanced energy-absorbing phases was designed. • The crushing stress–strain curve shows three stress plateaus, and BMAH maintains a stable Poisson's ratio even at high strain levels, transitioning from near-zero to negative and then to positive. • Under the selected material combination, the second stress plateau is 8 times greater than the first, and the third stress plateau is 17 times greater than the first, significantly improving energy absorption efficiency. • A theoretical model was established to reveal the deformation mechanism of BMAH and predict the plateau stresses and strain range for each deformation stage. • Effects of geometrical parameters and crushing velocity on BMAH stress plateaus and Poisson's ratio were investigated, and a programmable guide for designing stress plateaus and specific energy absorption is presented. The ideal energy absorption structures, in addition to possessing reusability and high energy absorption efficiency, should also possess multiple desired properties to fulfill various functional applications. In this study, a bi-material multistable auxetic honeycomb (BMAH) is fabricated by using bi-material 3D printing technology. Under in-plane crushing, multiple stress plateaus can be achieved and the Poisson's ratio can be stably tuned, allowing for a transition from near-zero to negative and then to positive. The above characteristics are attributed to the specimen's multi-path deformation. The first stress plateau is only associated with recoverable elastic deformation. The second and third stress plateaus, which are 8 times and 17 times higher respectively than the first, are associated with plastic deformation, significantly enhancing energy absorption efficiency. The deformation mechanism is theoretically analyzed, and the effects of geometric parameters on the performance of BMAH are investigated. In addition, the effect of crushing velocity on the crushing behavior of the BMAH is also discussed. As the crushing velocity increases, the total number of stress plateaus transitions from three initially to two and then to one. The developed BMAH exhibits significant potential applications in multi-stage energy absorbers and smart sensors. [ABSTRACT FROM AUTHOR]

• The proposed auxetic honeycomb possesses more excellent auxetic behavior and specific energy absorption than the conventional honeycomb. • The interaction between the structural parameters is analyzed. • The multi-objective optimization of the enhanced auxetic honeycomb (EAH) was investigated. • The theoretical model and Box-Behnken Design model were used to predict the mechanical properties of EAH. In response to the challenge of low stiffness and energy absorption capacity, various designs of negative Poisson's ratio (NPR) structures have emerged. However, these designs often lack a comprehensive analysis of other mechanical properties, leading to subpar mechanical performance. Previous studies have explored the mechanical properties response of enhanced re-entrant honeycombs (ERH) under impact conditions, revealing limitations in optimizing the structure's performance with a single objective. Therefore, this study aims to enhance ERH structural parameters to achieve superior mechanical performance through theoretical derivations and geometric optimizations. The results demonstrate that the proposed theoretical model is consistent with finite element analysis and response surface (RS) predictions. Expressions for Young's modulus, specific energy absorption, and compressive strength are proposed, facilitating the identification of structural parameters that meet specific requirements during reverse design. Furthermore, a multi-objective optimization approach optimizes the geometric parameters based on maximum energy absorption and compressive strength. The mechanical behavior of the optimized ERH is investigated using the finite element method, revealing the energy absorption capacity of 13.78 J/g while maintaining Poisson's ratio at -1.06. Additionally, the deformation mode of the optimized structure showcases enhanced stability compared to traditional honeycomb structures. The theoretical model and RS method were used to guide the design of ERH and promote the application of NPR structures. [ABSTRACT FROM AUTHOR]

• Introduced an optimized and expanded three dimensional steady-state transition structure. • Proposed a novel impact-resistant structure based on the steady-state transition design. • Demonstrated significant energy absorption features and energy oscillations in the steady-state transition structure under impact. • Highlighted the development potential of steady-state transition structures in the field of impact resistance. Advancements in materials science and mechanical system have spurred widespread investigation into non-traditional structures. In particular, engineers have shown interest in steady-state transition structures with phase transition properties. In this paper, a three-dimensional steady-state transition structure was established using the genetic algorithm and three-dimensional expansion, on which the low-velocity impact tests were carried out. Force response and energy absorption of the steady-state transition structures under impact were studied. From the force response and energy absorption curves, it can be seen that the steady-state transition structures absorb and store portion of impact energy temporarily, gradually releasing it after impact peak. This unique energy behavior results in a steady state transition structure with a long impact response time and a low peak impact force under impact. In addition, investigation into energy transfer within these structures reveals that energy oscillations occur among multilayered bistable surfaces during steady-state transitions, further improving the energy dissipation. Further, the dynamic response and damage modes of the honeycomb structure and the steady state transition structure were compared, showing that the damage mode of the steady state transition structure under the impact is an overall damage, in contrast to the penetration damage of the honeycomb structure. Notably, the steady-state transition structures showcase a higher proportion of elastic strain energy during impacts, effectively delaying structural damage onset, and dispersing impact energy, thus enhancing impact resistance. In light of these findings, the demonstrated behavior of steady-state transition structures in absorbing and dissipating impact energy showcases their potential as promising avenues for the development of more effective impact protection strategies. [ABSTRACT FROM AUTHOR]

In recent years, origami honeycomb metamaterials have garnered extensive attention from researchers. Re-entrant origami honeycomb metamaterials exhibit excellent mechanical performances by virtue of lightweight, high-energy-absorbing characteristics and diverse configurations. In this study, the gradient re-entrant origami honeycomb metamaterials are designed by changing significant geometric parameters. To investigate the effects of geometric parameters variations on compressive behaviors, the theoretical analysis model of the re-entrant origami honeycomb is built to predict the compression stress under low-velocity and high-velocity impact. Subsequently, the energy absorption of the uniform re-entrant origami honeycomb (UROH), the gradient-thickness re-entrant origami honeycombs (GTROHs) and the gradient-angle re-entrant origami honeycomb (GAROHs)are investigated under different compression velocities. The impact resistances of UROH, GTROHs and GAROHs are discussed systematically. By adjusting the gradient distribution of thickness, the deformation modes and Poisson's ratio curves of the structure could be altered. Furthermore, under the high-velocity impact, the specific energy absorption (SEA) of the unidirectionally negative GTROH is increased by 36% than that of UROH at the strain of 0.29. The SEA of the unidirectionally positive GTROH is higher by 14.4% than that of UROH at the strain of 0.8. In addition, the unidirectionally positive GTROH exhibits better impact resistance performance than UROH by comparing the peak stress and SEA value under different compression velocities. This study is expected to provide the new route for designing advanced origami-inspired honeycomb structures and improving buffer protection devices. • Gradient re-entrant origami honeycombs are proposed by varying significant parameter of cells. • An analytical model is established to estimate the plateau stress of the present structure. • Deformation modes and energy absorption of gradient origami honeycombs are investigated. • The crashworthiness of uniform and gradient re-entrant origami honeycombs are discussed. [ABSTRACT FROM AUTHOR]

• Honeycomb sandwich structures with continuous density gradients are designed. • Flexural behavior is sensitive to horizontal but insensitive to vertical gradients. • Achieved favorable flexural resistance with horizontal arched density distribution. • Detrimental effects from thin cover plates and honeycomb layers are indicated. Sandwich structures with graded cellular cores exhibit promising flexural performances, but their reliance on gradient continuity and distribution warrants further exploration. In this study, seven honeycomb sandwich structures with diverse continuous density gradients, encompassing horizontal, uniform and vertical variations, were designed based on the Voronoi technique and fabricated via 3D printing. Quasi-static three-point bending tests and numerical simulations were conducted to comprehensively analyze the flexural response of density-graded honeycomb sandwich structures. The results reveal a significant influence of the honeycomb core's density distribution on flexural performance, with pronounced sensitivity to horizontal distribution (perpendicular to the loading direction) and less sensitivity to vertical distribution. A favorable flexural resistance is achieved by strategically assigning higher relative density cells to the mid-span of a honeycomb core layer, gradually diminishing towards the ends, which was further optimized into an arched density distribution along the horizontal direction. The influences of cover plate and honeycomb thicknesses on the deformation mechanisms and energy absorption were also investigated, and indicate that thin cover plates and honeycomb layer have a detrimental effect on the bending load-bearing and energy absorption of the sandwich structure. [ABSTRACT FROM AUTHOR]

• A novel origami honeycomb acoustic metastructure is proposed as an effective impact energy absorber. • The metastructure features superior low-frequency sound and impact energy absorption capacities. • The origami foldcore and the top panel are the key components in absorbing impact energy. • Energy absorption efficiency of the metastructure can be enhanced by tuning its geometric parameters. The ancient art of origami has inspired the design and fabrication of numerous acoustic and energy-absorption mechanical metamaterials and metastructures. This study introduces an origami-inspired honeycomb acoustic metastructure designed for engineering applications that demand both high impact resistance and effective sound absorption. This acoustic metastructure is formed by bonding a panel containing periodically distributed perforated holes and a panel without perforations to a periodical array of trapezoidal origami-bellow units. Acoustic wave propagation and drop-weight impact simulations are conducted to investigate the acoustic performance and low-velocity impact behavior of the metastructure. The results show that the origami-bellow honeycomb structure exhibits superior sound absorption capacity over two frequency ranges, outperforming the conventional honeycomb-core sandwich structure. Furthermore, it is shown that, in comparison with both the conventional hexagonal honeycomb-core and the Miura-ori foldcore sandwich structures, the proposed acoustic metastructure demonstrates higher levels of impact resistance and energy absorption capacity. We also show that the mechanical performance of the introduced metastructure under low-velocity impact loads can be further enhanced by increasing the story height of the origami-bellow units. Besides, the matrix material of the origami foldcore can be tailored to suit various scenarios, providing noise control and collision robustness for a diverse range of engineering applications. [Display omitted] [ABSTRACT FROM AUTHOR]

• Out-of-plane stress-strain response of a sandwich panel differs from that of cellular core. • Adhesive height determines densification initiation strain. • Method correctly characterizes densification region, accounts for adhesive effect. • Significant energy absorbed in the densification region for panels with adhesive. • Larger fillets reduced the overall absorbed energy due to lower densification initiation strains. Lightweight aluminum honeycomb sandwich panels are widely used in industrial engineering, particularly in aircraft applications. Due to their thin-walled nature, the honeycomb cell walls are especially susceptible to buckling under out-of-plane compressive loading, while the adhesive fillet that secures the honeycomb to the face-sheet remains intact. This paper investigates the effect of the adhesive geometry and bonding constraints on the out-of-plane compressive response through experimental, Finite Element (FE), and mathematical methods. A hybrid method accounting for adhesive bonding between the face-sheet and the cell walls, and different adhesive fillet geometries was proposed to predict strain onset and stress-strain relationships during densification. The resulting stress-strain curves predicted the energy absorbed by the panels to within 3.5 % of the experimental results. The widely used material model for honeycomb core does not account for densification and underpredicted the absorbed energy by 15.6 %. These findings emphasize the need for detailed adhesive analysis in the design of lightweight, thin-walled sandwich structures. [ABSTRACT FROM AUTHOR]

• A novel re-entrant double-arrow auxetic honeycomb was proposed. • Three typical deformation modes under different impact velocities were revealed. • Theoretical models of single-plateau and double-plateau stresses were established. • The effects of impact velocity and geometric parameters were explored. A novel re-entrant double-arrow honeycomb (RDAH) has been proposed and investigated by combining re-entrant hexagonal honeycomb and double-arrow honeycomb. Quasi-static compression experiments of 3D printed samples in different loading directions were carried out. Deformation modes and stress–strain response have been explored and identified. The corresponding finite element (FE) models were established and verified, and the dynamic crushing behaviors of RDAH were further investigated by FE simulations. The results show that RDAH has three typical deformation modes under different impact velocities. When subjected to quasi-static loading and low-velocity impact along the horizontal wall, two stress plateau regions of the stress–strain curves can be observed, while there is only one stress plateau when loaded perpendicular to the horizontal wall. Based on deformation modes, theoretical models of plateau stresses of RDAH under low-velocity and high-velocity impact were further established. The theoretical results of the plateau stresses agree well with the FE simulation results. The effects of impact velocity and geometric parameters on densification strain, Poisson's ratio and energy absorption were also discussed. The results show that the RDAH exhibits obvious negative Poisson's ratio effect in both directions. The energy absorption of RDAH is higher when loaded along the horizontal wall and can be 29.45 % higher than the traditional RH structure. The energy absorption of RDAH increases with the decrease of inclined wall l 1 , the decrease of inclined angle θ (perpendicular the horizontal wall), and the increase of inclined angle θ (along the horizontal wall). [ABSTRACT FROM AUTHOR]