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• A central self-similar strategy is proposed to develop bio-inspired honeycombs. • Central self-similar degradable polymer honeycombs are additively manufactured. • The interaction effect of different connections between the two walls can promote EA. • Theoretical models of the proposed central self-similar honeycombs are built. At present, improving the energy absorption capacity of lightweight degradable polymer honeycombs is crucial for one of the future engineering applications and bio-inspired strategy based on hierarchy is considered an efficient method for designing honeycomb structures. To improve the energy absorption performance and stability of polymer honeycombs, this study develops three central self-similar bio-inspired honeycombs combining the microstructure of horsetails and designs different connections between the two walls and connecting structures for the central self-similar honeycombs. Bio-inspired honeycombs are fabricated using toughened polylactic acid (PolyMax™ PLA) through fused deposition modelling and subjected to axial compression tests. The finite element (FE) models of the bio-inspired honeycombs are developed to simulate the axial compression process and verified with experimental results. Results show that the connecting structures distributed on the outer wall of the central self-similar honeycombs considerably improve the energy absorption performance of the bio-inspired honeycombs. In the double-cell honeycombs, connecting structures interact with the cell walls, leading to the formation of more folding lobes on the cell walls and increased cell wall utilisation. Furthermore, the effects of geometrical parameters on the energy absorption performance of the bio-inspired honeycombs are investigated. Suitable connecting structure size and cell wall thickness can improve the energy absorption performance and stability of the honeycombs. In addition, the theoretical calculation models of the three bio-inspired honeycombs are established, and the errors with the FE calculation results are within 6 %, which verifies the accuracy of the theoretical models. [Display omitted] [ABSTRACT FROM AUTHOR]

• A cost-effective fabrication method is proposed. • More pronounced NPR effects can be attained by implemented misplaced design. • The comparative method of specific plateau stress is proposed. • The optimized MRHC structure possesses an excellent energy absorption performance. Two-stage plateau stress structures have emerged as a novel research focus in the field of impact protection and energy absorption. The proposal of structures exhibiting a two-stage plateau stress region is increasingly prevalent. However, the majority of currently available two-stage plateau stress structures are predominantly fabricated using 3D printing technology, which can incur substantial costs. Additionally, the majority of currently proposed two-stage plateau stress structures exhibit diminished plateau stress values and possess limited capabilities for energy absorption. The objective of this study is to develop an economically viable metamaterial that exhibits dual high-level plateau stresses and demonstrates exceptional energy absorption capabilities in two in-plane directions. Based on the concept of misplaced design and traditional reinforced honeycomb structures (RHC), a novel metamaterial named misplaced reinforced-honeycomb (MRHC) has been developed. Aluminum alloy component and stainless stee component are fabricated. After the implementation of the misplaced design, the MRHC structure exhibits a pronounced enhancement in negative Poisson's ratio effect. The influence of misplaced design on the mechanical performance of the MRHC structure, as well as the impact of horizontal cell wall length (l 3) and rotation angles (α and β), has been investigated. The multi-objective optimization has been employed to determine the optimal rotation angles α and β. The optimized MRHC structure was compared to the previously proposed two-stage plateau stress structures, revealing its superior energy absorption capabilities in both the in-plane X and Y directions. The proposed MRHC structure exhibits promising potential for future applications in impact buffering and collision protection fields. [Display omitted] [ABSTRACT FROM AUTHOR]

• Novel design strategy with cost-efficiency of multi-cell structure for energy absorption. • Shape of node-locked cell can be expanded for NMH. • Various bending shape selected for on-demand design of the node-locked effect. • Irregular localized deformation is beneficial to energy absorption of NMH. Material reconfiguration at node positions is currently a prominent method for enhancing the energy absorption capability of honeycomb structures. However, the complexity of cellar configuration poses challenges in the manufacture with cost-efficiency due to intricate preparation processes, which limits its widespread application. In this work, an innovative approach was proposed to fabricate the multi-cell honeycomb structure by nesting and assembling node-locked components with a specific shape. The stable energy absorption of multi-cell structure with node-locked design strategy was preliminarily validated by the numerical and experimental results. Additionally, the effect of the bent panels number and the cell size ratio were investigated numerically and theoretically to reveal the energy absorption mechanism of node-locked multi-cell honeycomb (NMH). It is demonstrated that the strategy by assembling node-locked components can significantly simplify preparation processes of multi-cell structure while maintaining excellent energy absorption capabilities, this offers a better balance between the cost-efficiency and superb energy absorption for multi-cell structures. [Display omitted] [ABSTRACT FROM AUTHOR]

• Face-centered hierarchical strategy is proposed to develop a novel honeycomb. • Face-centered hierarchical network provides strong lateral support to resist the multi-crushing loads. • Effect of hierarchy order and thickness gradient is significant on the multi-crushing properties. • Face-centered hierarchical honeycomb possesses the more stable and efficient multi-crushing properties. The undesirable resistance to multi-crushing loads limits the development of regular honeycomb structures in advanced engineering fields. Therefore, a novel hierarchical strategy, namely face-centered hierarchical strategy, is proposed to improve the multi-crushing properties of honeycombs. The honeycombs with the face-centered hierarchical network are manufactured by selective laser melting to test their energy absorption mechanism against the oblique crushing load. The multi-crushing properties of face-centered hierarchical honeycomb (FCHH) are explored by a numerical investigation. The carrying capacity and energy absorption of the FCHH decrease with the increasing crushing angle. The parameter configuration design indicates that the hierarchy order has a positive effect on the multi-crushing resistance of the FCHH. The face-centered hierarchical network not only provides the strong lateral support, improving the collapse of the honeycomb, but also reduces the folding wavelength, improving its material utilization. Specifically, the specific energy absorption and crushing force efficiency of the FCHH improve by 27.65 % and 30.83 % respectively as the hierarchy order increases from 1 to 3 at the crushing angle of 30°. Furthermore, when the thickness gradient factor is close to 1, the FCHH obtains a more reasonable material distribution to resist the oblique crushing load. Compared with other hierarchical honeycombs for the oblique crushing resistance, the FCHH demonstrates a more stable carrying process and more efficient energy absorption. This research expects to propose a promising reinforcement strategy to guide the design of multi-crushing properties for honeycombs. [Display omitted] [ABSTRACT FROM AUTHOR]

• Three novel lattices by inserting honeycomb struts into the traditional 3D auxetic structure were proposed. • The tensile and compressive mechanical behaviours of hybrid lattices were studied and compared. • 3D hybrid lattices are more effective in tension-dominated applications. Lattice structures have the potential for application in tensile conditions. However, limited studies have addressed tensile behaviours of such structures and compared them with their compressive behaviours. In this paper, re-entrant structure as the foundation was selected to develop new 3D hybrid auxetic honeycomb lattice structures, each characterized by a unique unit cell configuration that features interconnected centre auxetic honeycomb, differentiating it from 2D hybrid auxetic honeycomb structures. A series of uniaxial quasi-static tensile and compressive tests, followed by simulations were conducted on these structures to investigate and compare their energy absorption characteristics. The results show that there were significant differences between these structures in terms of their mechanical behaviours under tension and compression. Especially, the smallest value of energy absorption under tensile load was 86% higher than the largest value under compressive load. The stiffnesses of these lattice structures under tensile loading were about 84–122 times of those of the identical corresponding structures when they were compressed. Meanwhile, the progressive stretching, buckling and collapse mechanisms observed in these structures exhibited excellent stiffnesses and energy absorptions under tensile and compressive load compared to traditional 3D auxetic as the basic structure. The outer frame structure of lattice structures had a direct influence on Poisson's ratio. The work indicates that the stiffness and energy absorption of the traditional 3D auxetic structure can be enhanced by embedding auxetic and honeycomb umbrella shaped elements. [Display omitted] [ABSTRACT FROM AUTHOR]

• A novel EARE is designed by introducing an elliptical annular into RE cell. • EARE produces extra vertical support without hindering lateral deformation. • EARE concurrently enhances auxetic performance, stiffness, and SEA. • Adjusting geometric parameters rationalizes designing mechanical properties. Auxetic structures have sparked a lot of interest due to their excellent mechanical characteristics and unusual negative Poisson's ratio influence. However, the large porosity property results in low stiffness, which limits their application scope. Current approaches to augment stiffness often result in diminished auxetic performance. Therefore, it is challenging to simultaneously enhance the auxetic, stiffness and energy absorption capacity of auxetic structures. To address this issue, this paper proposes a novel elliptical annular re-entrant honeycomb (EARE) by introducing an elliptical annular structure into a conventional re-entrant honeycomb (RE) cell, which can provide extra longitudinal support without hindering lateral deformation. The plateau stress, Poisson's ratio and energy absorption properties of the EARE are investigated by quasi-static compressive tests and finite element modeling. The results show that the EARE honeycomb has two plateau stages due to the supporting effect of the elliptical annular structure. Compared with the conventional RE honeycomb with the same wall thickness, the EARE honeycomb not only exhibits a stronger auxetic effect embodied in the Poisson's ratio reduced by 5.19%, but also has a higher average plateau stress and a higher specific energy absorption of 171.63% and 28.03%, respectively, which significantly improves the stiffness and energy absorption performance. The parameterized analysis reveals that by appropriately adjusting the geometric parameters, the stiffness, energy absorption, and auxetic effect of the EARE honeycomb can be enhanced. The research findings address the conflict between auxetic performance and honeycomb stiffness, providing new insights into the optimization of honeycomb structure design. [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]

• Novel REAT honeycomb structure derived from bio-inspired gradient-based distribution. • Extensive experiments were conducted to decipher different stages of compression and mechanical properties. • Discovery of a new driver for deformation based on the difference in negative poisson's ratio between layers. • Uncovered 80% higher elastic stiffness and 20% larger densification strain for Chiral-based gradient distribution than its conventional counterpart. • Early-stage compression demonstrated 60% more plateau stress and constant 25% higher energy absorption efficiency. This study focuses on the nature-inspired gradient-based approach to re-designing re-entrant anti-trichiral (REAT) honeycombs through extensive experimental quasi-static compression. Novel perspectives on REAT honeycomb are offered through the introduction of gradient distributions on two critical geometrical parameters, the cylindrical diameter (chiral) and height of the unit cell, rather than the traditional thickness-based gradient approach. Chiral-based gradient approach demonstrated clear advantages in elastic stiffness, specific energy absorption (SEA) and densification strain over uniform REAT structures of constant geometrical parameters. These advantages are exhibited in their extended and constantly increasing quasi-plateau stage, consistent specific energy absorption (SEA) especially during early stages of compression, and most importantly, the ability to maintain a relatively constant energy absorption efficiency that is 25% more than that of the Base uniform REAT structure. Height gradient-based REAT structures, on the other hand, were able to leverage on associations between the negative Poisson's ratio (NPR) effect and height of unit cell to demonstrate notable deformation patterns across various portions of the structure. The present work reveals the performance enhancements through alternative gradient-based approaches over thickness-based gradient approaches and highlighted the differences in NPR between layers as the main driver of compressive collapse apart from the commonly concluded difference in relative density. [Display omitted] [ABSTRACT FROM AUTHOR]

• The proposed hybrid AuxHex structure consists of auxetic and honeycomb cells. • The equations for modulus and strength along x - and y -directions are derived. • Theoretical results are in agreement with simulation and experimental results. • Mechanical properties and specific energy absorption are enhanced 16% and 38%. The architected mechanical metamaterials have garnered significant research attention for a variety of engineering application due to their remarkable mechanical properties and unique deformation behavior. Herein, the in-plane uniaxial compressive response and energy absorption capacity of a novel hybrid configuration, AuxHex structure, which consists of auxetic and hexagonal honeycomb cells, are systematically investigated through theoretical, finite element simulation and experimental methods. A series of AuxHex sandwich core panels have been fabricated with nylon material by using additive manufacturing route. The relationships for Young's modulus and plastic collapse stress along different loading directions are derived and validated through the comparative analysis. In addition, the deformation mechanism and failure modes of the AuxHex structure have also been discussed in detail. The AuxHex structures have exhibited superior Young's modulus, collapse strength and energy absorption than traditional honeycomb structures. In the x -direction, the energy absorption capacity was improved by 38%, which can be attributed to the uniform and stable deformation mode of the unit cell. The theoretical prediction results of Young's modulus and plastic collapse stress are consistent with finite element simulation and experimental results. The AuxHex structures demonstrate a novel design strategy for the architected metamaterials through the combination of various cellular cells. The hybrid structures will play an important role in both the load-bearing and energy-absorbing applications, and it demonstrates a novel design strategy for the architected metamaterials through the combination of various cellular cells. Image, graphical abstract [ABSTRACT FROM AUTHOR]

A novel hierarchical re-entrant honeycomb metamaterial is proposed by integrating the re-entrant honeycomb (RH) with square unit cell and named as square re-entrant honeycomb (SRH). The novel hierarchical re-entrant honeycomb can not only improve energy absorption capacity but also present better vibration insulation compared with traditional RH structure. Dynamic crushing behaviors of the SRH structures are investigated theoretically and numerically. The theoretical plateau stress is in good agreement with the numerical plateau stress. Meanwhile, the deformation modes and energy absorption capacity of RH and square re-entrant honeycombs (SRHs) are compared under different impact velocities. The results show that the plateau stress and the specific energy absorption (SEA) of SRHs is higher than RH. Moreover, the vibration isolation capability of the SRHs is studied using finite element analysis. In particular, the introduction of square unit cells expand the band gap, especially in the low frequency range. By adjusting the size of oscillators, the starting and stopping frequencies of band gaps are lower effectively and the number of band gaps is increased. The results indicate that the introduction of the mass inclusions can improve the band gap characteristics of the SRH, which produce local resonance effect and the local resonance type band gap. It also appears multiple band gaps at the same time. In addition, the introduction of the mass inclusions also improves the SEA of the SRH under high-velocity crushing. This work may benefit structural vibration isolation and protection design, which provides a new thought for design and development of advanced multi-functional composite structures and materials in the engineering. [Display omitted] • A novel dual-functional metamaterial is proposed by integrating the re-entrant honeycomb with square unit cells. • The energy absorption capacity of the present metamaterial is investigated theoretically and numerically. • Band structure and vibration transmittance of the present metamaterial with or without local resonant inclusions are considered systematically. • Band gap and energy absorption performance of the present metamaterial with local resonant inclusions are researched. • The novel hierarchical re-entrant honeycomb metamaterial has enhanced energy absorption and excellent vibration insulation. [ABSTRACT FROM AUTHOR]

• An aluminum foam filled re-entrant aluminum honeycomb structure (FRAH) is designed and investigated. • The proposed FRAH possesses higher specific energy absorption compared to the structure without filling aluminum foam. • The concept of the functional gradient (FG) is introduced into the composite re-entrant honeycombs. • 4. The FG design of the composite structure could reduce the initial peak stress and increase the platform stress value. Auxetic materials have been widely studied in recent years due to their excellent mechanical properties and special deformation modes. However, the application of auxetic materials in practical engineering is limited by the low stiffness. Therefore, in order to broaden the range of applications, it is significant to improve the stiffness of auxetic materials. In this study, the re-entrant aluminum honeycomb is combined with an aluminum foam. The mechanical properties and deformation modes of the aluminum foam filled re-entrant aluminum honeycomb are studied experimentally and numerically. In addition, the effects of the geometrical parameters of such a honeycomb are investigated. The results indicate that the stiffness and the energy absorption capacity can be effectively improved by filling the re-entrant honeycomb with aluminum foam. Due to the high compressibility of aluminum foam, the structure can still retain the auxetic effect at a large strain. In addition, the concept of the functional gradient is introduced into the field of composite re-entrant honeycomb, and the influence of angle gradient and thickness gradient on the structure is analyzed. The results show that the composite structure with the designed functional gradient outperforms the uniform composite structure in terms of initial peak stress and the stress value at the platform stage. Due to its superior performance, the proposed auxetic composite structures hold promising applications in the fields of vehicle engineering, protective engineering and aerospace engineering. [Display omitted] [ABSTRACT FROM AUTHOR]

• Metallic graded RECH prototypes fabricated through a low-cost step-by-step method. • Graded RECH takes advantage of structural hierarchy and functional gradient. • Gradient design causes multi-step deformation mode and multi-plateau stress. • Improved SEA and auxeticity of graded RECH under different crushing velocities. As lightweight energy-absorbing materials, auxetic honeycombs have demonstrated promising applications in engineering fields. In this study, the graded re-entrant circular auxetic honeycombs (RECH) were proposed, and their metallic prototypes were fabricated through a low-cost step-by-step method. The novel design of graded RECH takes advantage of structural hierarchy on the meso-scale and functional gradient on the macro-scale. The in-plane crushing behaviors of uniform (U) RECH, positive gradient (PG) RECH and negative gradient (NG) RECH with the same relative density were investigated under different crushing velocities. The finite element (FE) models were validated by comparing against the experimental and theoretical results. The results showed that the gradient design can control the multi-step deformation modes of RECH, which leads to the multi-plateau characteristics and reduced initial stress peaks in stress-strain curves. Under quasi-static crushing, the specific energy absorption (SEA) of PG-RECH is higher by 43.9% than that of U-RECH owing to more plastic deformations of hierarchical circular walls at a large strain. Under dynamic impacts, the SEA of NG-RECH is 2.7 times and 1.5 times those of PG-RECH and U-RECH at a small strain, respectively. Finally, the NG-RECH shows more negative Poisson's ratio (NPR) behavior than the U-RECH under dynamic crushing. This study offers new routes to the fabrication and design of auxetic metamaterials. [Display omitted] [ABSTRACT FROM AUTHOR]

• A series of potential variable thickness honeycombs with enhanced biomimetic cells (VTHEBs) are proposed. • The crashworthiness mechanism of VTHEBs is revealed through experiments and simulations. • Theoretical models of VTHEBs under out-of-plane loading are developed. Honeycomb materials are often used as the inner core of composite sandwich structures and are widely applied in impact resistance equipment design. Inspired by biomimetic materials, a series of potential variable thickness honeycombs with enhanced biomimetic cells (VTHEBs) are proposed and analyzed in this study, including the variable thickness honeycomb with bionic circular cells (VTHBC), the variable thickness honeycomb with bionic triangular cells (VTHBT), and the variable thickness honeycomb with bionic hexagonal cells (VTHBH). The crashworthiness properties of VTHEBs are studied by experimental, numerical, and theoretical analysis. The experimental results reveal the mechanical responses of VTHEBs under out-of-plane loading and validate the numerical models established by LS-DYNA. It is also observed that VTHBC shows better crashworthiness than VTHBT and VTHBH. Compared with the corresponding regular variable thickness honeycomb (RVTH), the variable thickness honeycomb with enhanced bionic cells has superior material distribution, which helps to improve the crushing force level and energy absorption potential. Besides, the numerical models are used to explore the effects of different design parameters (thickness deviation coefficient, cell size coefficient) on the mechanical performances of VTHEBs. Finally, the theoretical models of crushing forces are derived to predict the crushing performances of VTHEBs. The results show that the theoretical models can approximate the overall trend of experimental and numerical results with acceptable accuracy. This study provides an interesting design concept for superior crashworthy structures, which can be expected to be applied to impact resistance equipment in the future. [Display omitted] [ABSTRACT FROM AUTHOR]

• Novel layered aux-hex honeycomb (LAHH) filled tube (LAHHFT) structures are designed and investigated. • Aux-hex interaction and LAHH-tube interaction lead to superior energy absorption performance. • Theoretical models are carried out to describe the double interaction effect. • Deformation modes of the LAHHFT structures are recognized and theoretically interpreted. In this work, a novel layered aux-hex honeycomb (LAHH) filled tube (LAHHFT) structure is proposed and investigated. A series of LAHH and LAHHFT structures with different number of aux-hex interfaces is designed and analyzed via extensive finite element analyses (FEAs). The results indicate that the designed LAHH and LAHHFT structures possess significantly higher effective Young's modulus, mean crushing stress (MCS) and specific energy absorption (SEA) than the single honeycombs and single honeycomb filled tubes under the same relative density. Double interaction effect, i.e. aux-hex interaction and LAHH-tube interaction, contributes to the superior improvement. Quantification of the interaction effect shows that the relative improvement of the MCS and SEA due to the double interaction effect could reach up to 617% and 557% for the LAHHFT structures. Theoretical models are carried out to predict the mechanical and crushing stress properties of the proposed hybrid structures considering interaction effect, which agree well with the FEA results. Besides, the interaction also affects the deformation modes of the LAHH and LAHHFT structures, which in turn influences the energy absorption performance. Three different crushing deformation modes including global bending mode, straight folding mode and mixed deformation mode occur to the LAHHFT structures. A theoretical model is also established and provides a good explanation to the change of deformation modes. This study offers a new route and a useful guideline for the design of future high-performance light-weight materials and structures. [Display omitted] [ABSTRACT FROM AUTHOR]

• A simple re-entrant auxetic metamaterial is designed by rotating and connecting 2D re-entrant honeycomb cells. • The energy absorption of the proposed metamaterial is discussed under different design parameters. • The proposed 3D re-entrant auxetic lattice has desirable stiffness and specific energy absorption. • The initial peak stress and energy absorption capacity of the metamaterial can be adjusted via changing design parameters. As a branch of auxetics, the re-entrant hexagonal honeycomb has many superior mechanical performances. However, most research focused on two-dimensional (2D) re-entrant structures or three-dimensional (3D) structures without high compressibility. The energy absorption capacity of such structures is deficient for practical applications. Therefore, it is important to investigate the 3D re-entrant honeycomb structures which can sustain large deformation in order to make the most use of the materials. In this work, a simple 3D re-entrant unit cell is designed, manufactured and examined. The influence of geometric parameters on the deformation mode and energy absorption capacity is investigated numerically. The experimental results are in good agreement with the finite element prediction. The proposed 3D re-entrant auxetic metamaterial not only possesses a greater bearing capacity but also presents a stable compression deformation. The structure exhibits a desirable energy absorption behavior, including obvious auxetic behavior and a long stress plateau. By adjusting the geometrical parameters of the structure, the performances of energy absorption and compression stiffness can be improved. These findings provide a new idea to design 3D auxetic metamaterials and promote their utilization in protective structures. [Display omitted] [ABSTRACT FROM AUTHOR]

• A novel Diabolo shaped honeycomb based on re-entrant hexagonal honeycomb is proposed. • Four enhanced honeycombs are designed based on the Diabolo shaped honeycomb by adding horizontal or longitudinal ribs. • The simulation results show that Diabolo shaped honeycomb has better impact resistance and energy absorption than re-entrant hexagonal honeycomb. • The plateau stress and specific energy absorption of the honeycomb are significantly influenced by the geometric parameters. This paper presents the design of a novel Diabolo shaped honeycomb (DSH) based on re-entrant hexagonal honeycomb (RHH), and four enhanced honeycombs are designed based on the DSH by adding horizontal or longitudinal ribs. The finite element software ABAQUS/EXPLICIT is applied to investigate the relationship between crashworthiness and energy absorption performance with different impact velocities and geometric parameters. The simulation results show that DSH has better impact resistance and energy absorption than RHH. DSH has improved plateau stress by 141.3%, 78.7%, and 22.7% of low-velocity, medium-velocity, and high-velocity compression, respectively, and SEA by 103.7%, 79.3%, and 7.3%, respectively. In addition, the impact resistance of the four enhanced honeycombs is further improved. The shrinkage effect of DSH after impact is not as good as that of RHH, and the horizontal ribs suppress the negative Poisson's ratio property of the honeycomb. Different impact velocities affect the deformation pattern of the honeycomb. With the increase of impact velocities, the honeycomb has a transition from overall deformation to local deformation with increasing velocity. The plateau stress and specific energy absorption of the honeycomb are significantly influenced by the geometric parameters. This research provides a reference for the optimal design and application of honeycombs as energy absorbing components. [Display omitted] [ABSTRACT FROM AUTHOR]

Cellular structures such as honeycombs are used to manage impact loads in many engineering applications, where often the impact load is oblique (non-axial). Although these structures have been extensively studied under axial impacts, a key question remains largely unaddressed: How may their axial and shear responses be independently tailored for oblique impacts? Here we test whether incorporating curvature in the form of axisymmetric shape changes in the cell walls of viscoelastic circular cell honeycombs enables independent control over their shear and compressive responses during oblique impacts. We developed detailed finite element models of the circular cell honeycombs made of the 3D printable viscoelastic material Agilus. Using a new rig, we validated the predictions of the finite element models under oblique impacts. We performed a full-factorial computational design-of-experiments, varying the cell shape from concave to convex with different amplitudes and impact velocities from 2.5 to 7.5 m/s in order to determine their effects on the shear and compressive responses of the honeycombs under oblique impacts. The finite element models demonstrate remarkable agreement with experimental oblique impacts for both concave and convex cells. Our full-factorial computational search shows that both convex and concave cells have similar compressive stresses. However, the post-buckling shear stress of the concave cells are up to 300% larger than the convex cells. In addition, increasing the impact velocity increases both compressive and shear stresses by 211% due to the viscoelastic nature of the material. Our results show that these new recoverable honeycombs provide a compelling control over their shear response under oblique impacts, which is nearly independent from their compressive response. These new honeycombs can be used to manage oblique impacts in a wide range of products, such as helmets, shoes and seats, where enabling an independent control over shear and compressive responses will open new design avenues. In addition, the proposed simple control mechanism, i.e. the curvature change, can be exploited in future to actively morph the honeycomb cells during use for real-time performance adjustment. [Display omitted] [ABSTRACT FROM AUTHOR]

• An innovative graded hierarchical honeycomb is proposed to improve its crashworthiness. • Two gradient distributions (negative & positive) and two sub-structural topologies (hexagonal & triangular) are considered. • Crushing mechanism of graded hierarchical honeycomb is investigated via numerical and theoretical analyses. • Specific energy absorption of graded hierarchical honeycombs is enhanced up to 32.2% as compared to uniform counterpart. • Three plateau stages can be observed for graded hierarchical honeycomb under dynamic crushing. Nature's bio-organisms are typically hybrid structures composed of hierarchical and functionally graded micro-architectures, which are lightweight and of high mechanical performances. Inspired by nature, an innovative graded hierarchical honeycomb is proposed in this study to enhance its crashworthiness behaviors. The structure is created by replacing cell walls of regular honeycombs with triangular and hexagonal sub-structures and varying the hierarchical length ratio in each layer. The in-plane crushing performances of the graded hierarchical honeycombs are comprehensively analyzed and compared with their uniform hierarchical counterpart. The former exhibits a progressive deformation model under different impact velocities and three plateau stages can be observed under in-plane crushing loads through theoretical predictions. The triangular sub-structure presents better energy absorption than the hexagonal sub-structure, and its specific energy absorption is enhanced by up to 32.2% as compared to the uniform hierarchical honeycomb. The present study suggests that the combination of hierarchy and gradient is an effective strategy to improve the dynamic crushing behaviors of honeycombs, which can be further explored in protective devices to enhance their impact resistance. [Display omitted] [ABSTRACT FROM AUTHOR]

This paper highlights the effects of cell wall material strain hardening and density functional gradation (FG) on in-plane constant-velocity dynamic crushing response and impact behavior of hexagonal honeycombs. Results show that cell wall material strain hardening influences the distinct deformation modes induced by crushing velocity generally observed in regular hexagonal honeycombs. This is seen by a delay in the onset of localized deformation up until intermediate crushing velocities after which localization becomes dominant smearing out differences brought about by cell wall material strain hardening ( plasticity convergence ). In addition, during the impact loading on regular honeycombs, it was found that increasing the cell wall material strain hardening decreases the rate of gain of maximum crushing strain with increments in initial kinetic energy of impact. On the other hand, introducing FG brings about new deformation patterns due to changes in material distribution and preferential cell wall collapse of the weaker members. Interestingly, although the dynamic localization effect at higher crushing velocities observed earlier was not found to be particularly affected by FG, gradient convergence (i.e. smearing out the effects of FG due to higher velocities analogous to plasticity convergence) was not observed. On the contrary, gradient convergence emerged at higher impacting velocities primarily brought about by a combination of initial deformation localization and its subsequent advancement into FG region ahead. The kinetic energy threshold for the emergence of this gradient convergence effect was found to be considerably delayed by cell wall material strain hardening. [ABSTRACT FROM AUTHOR]

l Designed methods of two kinds of honeycombs with curved cell walls are proposed. l The deformation mechanism is obtained by compression experiments and FEM method. l The mechanical properties of honeycombs are significantly enhanced. l Gradient can significantly improve the energy absorption performance of honeycombs. By replacing the cell wall of traditional rhombus honeycomb with a curved surface, two kinds of honeycombs with curved cell walls were designed and fabricated by fused deposition modeling(FDM) method. In-plane compressive experiments were conducted by the electronic universal testing machine to investigate the quasi-static mechanical response and deformation evolution of the specimens. Finite element models of the proposed honeycombs with different relative densities and gradient arrangements were established based on solid elements. Numerical simulations were performed by ABAQUS and the reliability of the numerical simulation results is verified by comparison with experimental results. Meanwhile, the effects of relative density and gradient type on the mechanical properties and energy absorption performance of honeycombs with curved cell walls were analyzed. It was revealed that with the relative density increases, the strength and relative stiffness of intersecting curved honeycomb(ICH) are significantly enhanced. The intersecting curved honeycomb(ICH) with a continuous gradient exhibits the best energy absorption performance compared with the conventional honeycombs. [Display omitted] [ABSTRACT FROM AUTHOR]