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The low stiffness resulting from substantial core porosity within the re-entrant honeycomb sandwich panel can be addressed by introducing rib-reinforcements. To investigate its static and vibration characteristics, an energy-based 2D equivalent-homogenization model (2D-EHM) was derived through asymptotic analysis of the leading terms in the governing equations considering the energy-related characteristics. The accuracy of the constructed model for predicting the elastic bending performance of the sandwich panel was verified by comparing the results of a three-point bending experiment with 3D-printed specimens. Comparative analysis with a 3D FE model demonstrates that the 2D-EHM exhibits maximum errors of only 4.65% and 6.46%, respectively, in analyzing static deformation and natural frequency while improving computational efficiencies by up to 59- and 173-folds. Parameter analysis reveals that the performance of SP-RRH is minimally affected by the reinforcement-to-honeycomb wall thickness ratio. However, its performance is compromised when the honeycomb walls align in an equilateral triangle with the reinforcing walls. Comparing specific stiffness as well as static and vibration characteristics of sandwich panels with different core configurations (including traditional and diamond reinforced re-entrant honeycombs) shows that inclusion of rib reinforcements enhances deformation resistance and natural frequencies through increased specific stiffness. These findings provide valuable insights for optimizing design of re-entrant honeycomb sandwich panels. [Display omitted] • VAM-based 2D model of SP-RRH accurately validated against 3D-FEM results. • Equivalent stiffness obtained via asymptotic analysis of unit cell's energy functional. • The tailorability of the unit cell facilitates the customization of its properties. • Rib-reinforcing walls enhance deformation resistance of sandwich panels. • The performance of SP-RRH is influenced by equilateral triangular cellular structure. [ABSTRACT FROM AUTHOR]

• 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]

• The tool-workpiece contact rate of the straight blade is systematically analyzed. • The theoretical model of fracture force at the blade edge is established. • The theoretical model of friction force on blade surfaces is established. • Reduction mechanism of cutting forces in ultrasonic cutting is revealed. Aramid honeycomb has extensive applications in the aerospace and rail transportation industries. Ultrasonic cutting (UC) with the straight blade (SB) is an advanced technology used for the profile machining of honeycomb materials. Cutting force is an important factor affecting machining quality, and its accurate modelling is particularly important. However, SB is a flake tool, and chips of honeycomb are removed in block or strip forms during cutting, and its structure and material removal method are obviously different from conventional machining. Existing simplified cutting force models based on kinematic analyses and experiments are incapable of describing the cutting process. In this paper, a geometrical kinematics analysis of SB is conducted. Further, the modelling of tool-workpiece contact rate (TWCR) for UC with SB is established, which is utilized to analyze the tool-material contact state. Based on the principle of conservation of energy, the fracture force at the blade edge is analyzed. Based on the analysis of instantaneous friction force, the friction force model on blade surfaces is established. Multiple-cutting experiments are conducted to separate fracture force and friction force. The influence of machining parameters (ultrasonic amplitude, lead angle, cutting speed) on TWCR, cutting force, fracture force, and friction force have been theoretically and experimentally studied, and the reduction mechanism of the cutting force is revealed. Furthermore, the machining quality under different machining parameters is observed and the relationship with cutting force is analyzed. The paper not only provides theoretical guidance for the study of the UC mechanism but also helps to guide the UC process of aramid honeycomb. [Display omitted] [ABSTRACT FROM AUTHOR]

• Innovative metamaterial design approach proposed to improve energy absorption capacity. • Varying the structural parameter (D/d) enhanced the metamaterial auxetic effect. • HPH metamaterials absorb energy effectively horizontally with their honeycomb structure. • HPH metamaterials show excellent reusability at lower compression ratios. Hexagonal perforated honeycomb (HPH) metamaterials were designed, fabricated and investigated in this work. Initially, the mechanical properties and deformation modes of various proposed HPH metamaterials (HPH-U, HPH-1 L and HPH-3 L) under quasi-static vertical compression were analyzed using experimental and finite element methods. The findings reveal significant improvements in mechanical properties and energy absorption due to the honeycomb and hierarchical expandable design. Notably, the auxetic effect is diminished. Subsequently, the impact of key dimensional parameters on the mechanical properties and Poisson's ratio behavior was explored. The results highlighted that an increase of elliptical perforation major axis to minor axis ratio enhanced the auxetic effect but compromised load-bearing and absorptive capacity. Additionally, HPH metamaterials displayed exceptional performance under quasi-static horizontal compression, with their honeycomb structure enabling them to withstand both vertical and horizontal impacts while exhibiting excellent energy absorption capabilities. The study also identified relative density as a crucial factor influencing horizontal impact performance. Finally, the study subjected the HPH metamaterials to multiple quasi-static vertical repetitive compressions, meticulously analyzing variations in mechanical properties under diverse compression ratios. Due to distinctive structural design and impressive mechanical properties, HPH metamaterials demonstrate immense potential for applications in automotive engineering and sports protection fields. [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]

The integration of two vertically crossed re-entrant honeycombs gives rise to a 3D re-entrant honeycomb (3D-RH), which displays intricate three-dimensional auxeticity. To simplify the modeling complexity, this study employs asymptotic analysis of the energy functional stored in the unit cell of the 3D-RH to develop unified constitutive models for 3D structures and panels with multiple length scales. Based on this, an equivalent 3D Cauchy continuum model is established for multi-layer 3D-RH, while a 2D equivalent plate model is developed for sandwich panel with single-layer 3D-RH (SP-3D-RH). The accuracy and effectiveness of these equivalent models are subsequently confirmed through investigations of the X-shaped compressive deformation of multi-layer 3D-RH, as well as the in-plane auxetic deformation and out-of-plane dome-shaped deformation of single-layer 3D-RH. Compared to traditional hexagonal and re-entrant honeycomb sandwich panels, the SP-3D-RH exhibited enhanced equivalent tensile stiffness while effectively mitigating maximum deformation and strain energy under bending and tension conditions. However, due to its relatively low equivalent shear stiffness, the SP-3D-RH exhibited significant deformation and strain energy when subjected to torsional loads, resulting in local stress concentration in the connect region between adjacent facesheets. Parameter analysis shows that the facesheet-to-strut thickness ratio had a substantial impact on the equivalent stiffness and in-plane behavior of the SP-3D-RH, while adjusting the horizontal strut length, strut depth, and re-entrant angle of the 3D-RH can improve the out-of-plane behavior. [Display omitted] • Equivalent models improve efficiency and accuracy in static analysis of 3D-RH. • 3D-EHM captures the X-shaped compressive deformation of multi-layer 3D-RH. • SP-3D-RH shows significant deformation and strain energy under torsional loads. • The facesheet-to-strut thickness ratio affects stiffness and behavior of SP-3D-RH. • 3D-RH in sandwich panel mitigates deformation under tension and bending. [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]

• Classification of the deformation modes of sandwich panels with Miura-ori cores is proposed. • An analytical meso‑scale model of panels' deformation with strong origami cores is developed. • The applicability of the homogenisation approach to the core material properties is analysed. • Experiments were conducted to validate the finite element studies and analytical models. • Comparison of the bending strengths of Miura-ori, PVC and honeycomb core panels is presented. Collapse mechanisms of sandwich panels with Miura-ori cores are analysed and classification of the deformation regimes under three-point bending is proposed. It is revealed that the homogenisation approach to the core material properties is not applicable to the deformation of panels with relatively strong origami cores due to the immediate simultaneous local deformations of the core and face sheets. To describe this deformation regime, an analytical model based on the development of new stationary hinge lines in Miura-ori cells and rigid motion rotation of the adjacent planes is proposed. The model pertains to a single degree-of-freedom model governed by the global bending angle of the panel. On the other hand, the homogenisation approach to the core material properties proved to be applicable to bending analysis of panels with relatively soft Miura-ori cores. This approach is used to analytically obtain the collapse load related to several deformation modes. Parametric FE analysis is conducted to further explore the deformation regimes of panels with different face sheet thicknesses. Experiments were conducted to validate the finite element studies and analytical models. A good agreement between the analytically predicted collapse forces and those obtained by the FE simulations is shown. Deformation mode maps are constructed based on the analytical and FE analyses in terms of the face sheet thicknesses and core strength. A brief comparison between the bending strength of sandwich panels with Miura-ori cores and panels with PVC and honeycomb cores is presented, demonstrating the superiority of the honeycomb cores loaded in the out-of-plane direction. On the other hand, the possibility of the development of high shear strains in metallic Miura-ori cores without damage gives them advantages compared to three-point bending of panels with low density PVC foam cores. [Display omitted] [ABSTRACT FROM AUTHOR]

The core layer of accordion honeycomb sandwich panel (accordion HSP) exhibits exceptional affinity for one-dimensional curvature deformations due to its special zero Poisson's ratio effect. This study thoroughly examines its static and dynamic characteristics by decomposing the analysis into unit-cell constitutive modeling and a two-dimensional equivalent-oriented model (2D-EOM) through the variational asymptotic method. The unit-cell constitutive modeling enables determining equivalent stiffness properties for the 2D-EOM. To validate the accuracy and efficiency of the proposed 2D-EOM, its results are compared against those obtained from a detailed 3D finite element model, including in-plane and out-of-plane behaviors of the core layer and sandwich panel, as well as free and random vibration under diverse excitation conditions. The comparison results demonstrate a significant three-fold increase in the equivalent stiffness of the accordion honeycomb in the direction of the added ligaments, as compared to the re-entrant honeycomb. Simultaneously, the acceleration amplitude of the accordion HSP is effectively reduced by 4% due to the involvement of lower high-order frequencies, rendering it exceptionally suited for shockproof meta-structural applications. This equivalent model not only fulfills accuracy requirements but also improves computational efficiency by 15 times, providing an effective approach for preliminary design of honeycomb sandwich panels. • Exceptional affinity for 1D curvature deformations due to ZRP effect of accordion core. • Comprehensive analysis of static and random dynamic characteristics of accordion HSPs. • Enhanced computational efficiency of 2D-EOM while maintaining sufficient accuracy. • Increased stiffness achieved by incorporating ligaments into accordion honeycombs. • Reduced acceleration amplitude due to involvement of lower higher-order frequencies. [Display omitted] [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]

• 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]

• We present an analytical model able to predict the effective elastic constants of SSHCs. • The model accounts for the effect of thick faces and assumes that the core is weak. • SSHCs are significantly stiffer than conventional honeycombs under in-plane loading. • SSHCs show reductions in the out-of-plane shear moduli of at least 10%. • For in-plane loading, the Gibson–Ashby exponents of SSHCs range from 1.6 – 1.8. Sandwich-structured honeycombs (SSHCs) are hierarchical structures comprising sandwiched cell walls and are known to exhibit enhanced mass-specific properties. Here, we present an analytical model capable of predicting the effective elastic properties of hexagonal SSHCs, employing a sandwich beam theory that accounts for the effect of thick faces and regards the core as structurally weak. The analytical solutions of the nine elastic constants are compared with the numerical predictions obtained from a finite element-based homogenization technique, and an excellent agreement is reported for a wide range of architectural parameters such as the beam size, core thickness, and angle. Overall, it is found that SSHCs outperform conventional (monolithic) honeycombs in terms of their in-plane elastic and shear moduli, reporting values up to 20 times the monolithic counterparts of identical mass. In contrast, the out-of-plane shear moduli of the SSHCs showed reductions of at least 10% as compared to the traditional monolithic honeycomb structures. [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]

• 3D bi-material triangle re-entrant honeycomb with adjustable Poisson's ratio is proposed. • The intrinsic mechanisms of tunable CTE and PR are revealed by theoretical models. • The finite element analysis is used to calculate the band structures and width of the total effective bandgap. • This work provides a design idea for 3D metamaterials to regulate CTE, PR and the bandgap. In the aerospace industry, precision components need to serve in a comprehensive environment of severe temperature changes, vibrations, and noise. Therefore, it is necessary to design a multifunctional mechanical metamaterial that integrates a tunable coefficient of thermal expansion (CTE), Poisson's ratio (PR), and bandgap. Here, a 3D bi-material triangle re-entrant honeycomb (3D-BTRH) with adjustable Poisson's ratio is proposed. Due to the geometric symmetry, the 3D-BTRH realizes the isotropy of mechanical properties in the three coordinate axes. The intrinsic mechanisms of tunable CTE and PR of the 3D-BTRH are revealed by building theoretical models. The accuracy of the theoretical analysis of PR and Young's modulus is verified by simulation and experiment. The finite element analysis is used to calculate the band structures and width of the total effective bandgap utilizing Bloch's theorem and Bloch's periodic boundary conditions. The accuracy of the band structure calculations is verified by calculating the transmission characteristic curve. The parametric analysis shows that the 3D-BTRH can achieve tunable CTE and PR in the directions of the three axes, and has a large width of the total effective bandgap. Moreover, this work provides a design idea for 3D metamaterials to simultaneously regulate CTE, PR, and the bandgap, which offers opportunities for better engineering practice. [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]

This study proposes a novel sandwich panel with an improved star-shaped honeycomb (SP-ISH) by replacing sharp corners with cubic struts and lengthening inclined ribs of traditional honeycomb. To more effectively analyze its special dynamic characteristics, the bending Poisson's ratio was derived and effective engineering constants were obtained through asymptotic analysis of the energy functional stored in periodic unit cells. Based on this analysis, a two-dimensional equivalent downscaling model (2D-EDM) was developed to investigate the free vibration of SP-ISH under various boundary conditions, and the influence of initial deformation on free vibration was also discussed. The frequency-domain and time-domain analyses were employed to identify the resonance characteristics of the SP-ISH under harmonic loading. Our findings demonstrate that 2D-EDM can accurately predict the free and forced vibration of SP-ISH and improve computational efficiency by reducing DOFs. The results indicate that the maximum resonance response was obtained by applying excitation at the center of the sandwich panel. Additionally, under cyclic loading, a sharp change in local stress amplitude was observed in the facesheet-core interface region. Compared with traditional star-shaped honeycomb, the incorporation of extended ribs and added struts could significantly reduce the maximum resonance amplitude by 3.8%. Notably, the natural frequencies of SP-ISH were affected by initial compression (up to a 40.6% reduction) and tensile deformation (up to a 26.4% increase). [Display omitted] • Improved SSH design with added cubic struts and elongated inclined ribs. • VAM-based 2D-EDM is developed for free and forced vibration of SP-ISH. • SP-ISH has superior dynamic characteristics other honeycomb sandwich panels. • Initial deformation from support movement impacts free vibration. • 2D-EDM accurately predicts resonance amplitude for various excitations. [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]

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]

• Novel bionic cores are proposed, whose unit cell is composed of sinusoidal beams. • Bionic cores improve the crashworthiness and load bearing capacity. • Theoretical model shows the relationship between force and geometric parameters. • The wall thickness, amplitude and number of cells can affect crashworthiness. In this paper, novel bionic sandwich cores are proposed based on the cross section of seagull feather shaft to provide an effective protective mechanism against impact. The relative density of the bionic core is firstly defined, which is closely related to cell configuration and geometric parameters. Through finite element simulations supported by experiments using 3D printed specimens, the novel bionic core is found to be superior in crashworthiness as compared to conventional honeycomb core in terms of specific energy absorption and mean force under out-of-plane compression. To decipher the underlying mechanisms for the enhanced performances, a theoretical model for the bionic core is derived based on the simplified super folding element (SSFE) theory. The effects of wall thickness, number of cells and amplitude of sinusoidal beam on relative density and crashworthiness are explored. It is revealed that the increase in wall thickness and number of cells led to improvements of load bearing capacity. An optimal structure is subsequently obtained based on the complex proportional assessment (COPRAS) and response surface method (RSM). Compared to conventional honeycomb core, the optimal peak force of the bionic core is decreased by 11.53%. Through the combination of experiment, simulation and theoretical analysis, this study provides a novel idea for the optimization of the crashworthiness of the bionic core under out-of-plane compression. [Display omitted] [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]

• A class of multistable shape-reconfigurable origami honeycombs are proposed. • The honeycomb has scalability in 3D space by tilling or tessellating. • The honeycomb is lightweight and owns flexible and easy designability. • A simplified rod-hinge model can easily predict the behavior of the bistable unit. Increasing energy and space utilization efficiency is crucial for lightweight shape-reconfigurable materials/structures that require tunable functions and multiple applications. Mechanical multistable origami/kirigami structures can improve the controlling stability and energy utilization efficiency of shape-reconfiguration. However, their scalability in 3-dimensinal (3D) space by tilling or tessellating remains largely unexplored. Inspired by origami, we propose a class of novel multistable shape-reconfigurable honeycombs that are lightweight, scalable in 3D space and have flexible and easy designability. It is architected by periodically arranged truncated diamond-shaped units composed of crease-connected panels. Each unit has two stable states, i.e., the deployed state and collapsed state, which can switch from each other reversely and repeatedly. Firstly, the bistability and mechanical tunability of the unit are verified by experiments. Then a simplified rod-hinge model for investigating the mechanical behavior of the unit is established and validated numerically. Based on this simplified rod-hinge model, the effects of edge number and geometric parameters of the unit on its mechanical behaviors are studied. This novel design and its mechanical model may pave a new way for the design and analysis of lightweight shape-reconfigurable materials/structures. [Display omitted] [ABSTRACT FROM AUTHOR]

· A bi-material triangle re-entrant honeycomb (BTRH) with the tunable coefficient of thermal expansion (CTE), poisson's ratio (PR), and bandgap is proposed. · Analytical analysis and numerical simulations are implemented to quantify the evolution of the effective CTE, PR, and young modulus. · The band structures of the BTRH are calculated by finite element analysis. · The effects of geometric parameters and material combinations on the mechanical properties are investigated. The future mechanical metamaterials should achieve multifunctional integration to meet the requirements of structures and materials in the aviation field for service in complex environments. In this paper, a bi-material triangle re-entrant honeycomb (BTRH) with the tunable coefficient of thermal expansion (CTE), Poisson's ratio (PR), and bandgap is proposed. Analytical analysis and numerical simulations are implemented to quantify the evolution of the effective CTE, PR, and Young's modulus. Experiments are conducted to verify the correctness of the theory of the effective PR and Young's modulus. Based on Bloch's theorem, the band structures of the BTRH are calculated by finite element analysis, and the correctness of the band structure calculation is verified by calculating the transmission characteristic curve. The effects of geometric parameters and material combinations on the mechanical properties are investigated systematically. The results of analytical and numerical simulations exhibit that the CTE and PR can be coupled with regulation from positive to negative through changing the geometry configuration and material combinations of the BTRH. Meanwhile, the function of tunable bandgap and large total effective bandgap width can be obtained. This work provides an important reference for the rational design of multifunctional metamaterials to maintain shape stability and efficient sound insulation. [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]

• Elasticity and failure behaviors of the resin-coated aramid paper are analysed. • A novel segmented equivalent mechanical model of the material is proposed. • Equivalent mechanical parameters of multi-layer structure are derived theoretically. • Proposed model performs well in ultrasonic cutting simulation of Nomex honeycomb. • Difficulty of modelling and CPU time of simulation are reduced significantly. Nomex honeycomb, as the core part of sandwich structure, has been widely used in the aviation and aerospace industries. Ultrasonic cutting, as a technology that can reduce machining defects, has been highlighted in recent years, but some problems in the cutting process still need to be investigated significantly. Finite element method (FEM) offers an alternative way of in-depth understanding of the problems. However, the multi-layer structure of the Nomex honeycomb cell wall, which is the resin-coated aramid paper, makes it difficult to establish a detailed multi-layered finite element (FE) model at a macro-scale level. Therefore, a novel segmented material mechanical model, which is applicable to the equivalent single-layer model, is proposed based on the analysis of the mechanical behaviour of the multi-layer structure of the resin-coated aramid paper. Moreover, the calculating method of equivalent mechanical parameters of the multi-layer structure are proposed theoretically. The proposed method is first verified by FE models at a micro-scale level in both single-layer and multi-layer approaches. Additionally, simulations and experiments are performed to verify that the proposed method performs well in the simulation of ultrasonic cutting for Nomex honeycomb, and the difficulty of modelling and CPU time of simulation are reduced significantly. [Display omitted] [ABSTRACT FROM AUTHOR]

• Modular strategy for flexible, efficient and adaptive crashworthiness was proposed. • The omnidirectional self-locking capability was possessed. • The crashworthiness was enhanced by discrete auxetic locking points. • The mechanical properties could be on-demand tuned. • The adaptivity to complex protection requirements was observed. The mechanical properties of most impact-resistant devices cannot be flexibly adjusted after manufacture to adapt to complex engineering requirements. Honeycombs are widely used due to excellent crash performance, while sharp initial peak stress under out-of-plane impacts results in great damage, and their in-plane bearing capacity is significantly weaker. To break these limits, flexible, efficient and adaptive impact-resistant metamaterials were discretely assembled using thin-walled modules to provide omnidirectional self-locking capability without applying constraints. Discrete auxetic locking points are formed among adjacent modules by introducing grooves, leading to crashworthiness approaching out-of-plane loaded honeycombs, and the impact peak stress is effectively attenuated. The assembling and disassembling processes of metamaterials are proven convenient, endowing them with on-demand property tunability to adapt to load characteristics through controlling basic parameters and distributed arrangement of modules. The metamaterials display isotropic stiffness in principle directions, and can adjust to enhance the stiffness in specific direction without increasing equivalent density. Furthermore, the metamaterials possess imperfection insensitivity to eliminate the damage of assembly errors in emergencies, and their shape and size can be feely customized to adapt to protected object geometry. This research opens a new avenue for designing metamaterials with efficient mechanical behavior and flexible property tunability. [Display omitted] [ABSTRACT FROM AUTHOR]

We present a reconfigurable electro-elastic topological insulator that produces a new valley phase with a large Chern number. This piezoelectric metamaterial comprises a hexagon-like honeycomb structure and periodic bonded piezoelectric beams. The composite piezoelectric Mindlin plate formulation in the isogeometric analysis is employed to calculate the band structure. A Dirac cone can emerge at the K point due to the C 3 v symmetry of the primitive element. Nontrivial topologically protected bandgaps develop after breaking mirror symmetry with the adding-on negative capacitance circuit. Additionally, we demonstrate that the topological quantity in this system arises in a large valley Chern number of one. The domain wall will exhibit two edge states between different topological microstructures according to the bulk-edge correspondence principle. The shielded transport of flexural waves is highly resistant to structural disturbances such as sharp corners or cavity flaws in the proposed metamaterial, resulting in a novel strategy for the reconfigurable electro-elastic topological insulator. [Display omitted] • A new valley topological insulator with large Chern numbers is discovered in the elastic system. • This new elasitc insulator exhibits two distinct topological edge states at each interface. • The piezoelectric shunts can be employed to tune propagation path of the edge states. • The composite piezoelectric Mindlin plate formulation of the isogeometric analysis is developed. [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]

• The fibers of the abdominal segment are distributed as helicoidal hollow tubes. • Laser powder bed fusion fabricated helicoidal structure has high forming quality. • Energy absorption of helicoidal structure is 2.4 times that of honeycomb structure. • The helicoidal structure has a unique twisting stress conduction mechanism. Abdominal segments are common in crustaceans and are used as biological armor to provide mechanical protection from the surrounding environment. However, little is known about the abdominal segments. Mantis shrimps, a group of crustaceans, evolved abdominal segments that are mechanically robust. Here, we conduct a systematic study of the three-dimensional geometry, material composition, nanoindentation mechanical properties, and microstructural features of mantis shrimp abdominal segments. Inspired by the helicoidally distributed fiber hollow tubes of abdominal segment, a mechanically efficient helicoidal structure is designed and fabricated by laser powder bed fusion (LPBF). The LPBF processed helicoidal structure achieves high forming accuracy (peak deviation = 7.5 μm) and relative density (99.78%). Furthermore, using a combination of compression experiments and finite element simulations, we show that the helicoidal structure exhibits superior specific energy absorption (2.4 times) and plateau stress (2.7 times) to the conventional honeycomb structure and tube structure. The structural optimization results show that the rotation angle and the number of layers have a significant effect on the mechanical properties and the helicoidal structure with a rotation angle of 45° and 3 layers has the best comprehensive energy absorption performance. We demonstrate that the mechanism for this improvement in mechanical properties is the unique twisting stress conduction path of the helicoidal structure under compression. Our results reveal that bio-inspired additive manufacturing paves the way to develop high-performance structures which are in great demand in modern industrial applications. [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]

• This study explores the synergistic effect of shear-thickening fluid in honeycomb. • It incorporates detailed analyses of various often-neglected geometrical and rheological parameters. • Effects of these parameters on plastic and viscous energy dissipation are studied. • The relationship between the mean crushing force contributed by STF and loading velocity is presented. • The optimal honeycomb thickness and STF viscosity are crucial to avoid undesirable pre-mature densification. Shear thickness fluid (STF) is considered an ideal filler to enhance the mechanical behaviour of in-plane honeycomb due to its special rheological properties. In order to investigate the dynamic compressive behaviour of STF-filled honeycomb, a comparative study between a STF-filled honeycomb and an empty honeycomb is numerically carried out after the fluid-structure coupled model has been validated against experimental testings. It is shown that the addition of STF in the honeycomb cells results in significant improvement in the energy absorption of the STF-filled honeycomb, which in turn, effectively prevents the premature collapse of the honeycomb cell walls. Furthermore, a parametric study of STF-filled honeycomb is conducted to investigate the contributions of each component to the total energy. It is found that the honeycomb plastic deformation is the predominant mechanism of energy absorption during impact, whilst the proportion of viscous energy contribution to the total energy is significantly reduced when the honeycomb wall thickness is increased. Additionally, the mean crushing force of STF-filled honeycomb has a power law relation to the honeycomb wall thickness for each specific loading velocity. Moreover, the mean crushing force contributed by STF is proportional to loading velocity and the increase in velocity significantly improves the percentage of viscous energy to the total energy. Meanwhile, optimal honeycomb thickness and weight fraction of STF are crucial to avoid earlier plastic densification of the honeycomb during the loading process. The results of this paper provide useful insights for future design and optimization of STF-filled structures. [Display omitted] [ABSTRACT FROM AUTHOR]

A bi-factorial hierarchical strategy is proposed to obtain a superior crushing resistance by optimizing the network section of honeycomb materials. A novel honeycomb named bi-factorial hierarchical honeycomb (BFHH) is developed, and its promising energy dissipation mechanism and progressive folding deformation are revealed by a compressive experiment. In the crashworthiness comparison, the material utilization and the crushing load efficiency of the BHFF- c 16 - h 2 are superior to those of honeycombs with other hierarchical types with the same mass. Furthermore, a crashworthiness design on the bi-factorial hierarchical honeycomb is conducted to explore the effect of geometric parameters on crushing resistance. The increasing hierarchical factor h can improve the energy dissipation mechanism of the BFHH. The thickness-length ratio t/l can determine the deformation mode of the BFHH, which further controls the crushing loading efficiency of the BFHH. In addition, a dynamic matching strategy for the effective crushing distance coefficient is proposed to optimize the accuracy of theoretical analysis. The error of theoretical derivation is controlled to within 7%. Research findings can provide a guiding significance for the crashworthiness design of honeycomb materials. [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]

• The combined effects of bending curvature, loading angle, and thickness on the crushing response of curved honeycombs were clarified in detail. • A macroscopic yield criterion for the initial yield stress of curved honeycombs was presented. • A novel inverse parameter identification method was proposed for the macroscopic yield criterion of curved honeycombs. This paper investigated the initial yield behavior of curved honeycombs under combined shear-compression loads with particular attention to the curvature, loading angle, and honeycomb thickness effects. A detailed finite element model was introduced to analyze the mechanical response and deformation mechanism of curved honeycombs and then verified through experiments using a specially designed set-up. It was found that the curvature had a significant effect on the crushing response. As the curvature increased, the initial peak stress reduced by 16.20%. The out-of-plane loading angle ranging from 0º to 15º had little effect on the crushing behavior, whereas it became more pronounced for the angles larger than 15º. In comparison, the effect of in-plane loading angle fluctuating between 0º and 60º was more significant. Based on the obtained data, a macroscopic yield criterion for the initial yield stress of curved honeycombs was proposed. A novel inverse parameter identification approach for curved honeycombs was proposed to determine the induced parameters conveniently. The current study gave insight into the performance change of honeycombs with specific curvature and could be used to develop its constitutive models under complex loads. [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]

• Impact behavior of tailored honeycombs with bilinear wall-thickness gradients is studied. Tailored honeycombs were realised via Digial Light Processing AM. • Bilinear cell-wall thickness gradients enhance energy absorption up to 250%. • Tailored honeycombs enhance both impact resistance and energy absorption concurrently. Enhancing the energy absorption characteristics of a material/structure without compromising its strength and stiffness has been a longstanding challenge in the pursuit of lightweight engineering. Here, we introduce a novel tailoring strategy where the wall thickness of the honeycombs is bi-linearly graded along the out-of-plane direction to tune their energy absorption and impact resistance by varying two design parameters, the gradation parameter α and the normalized taper length η '. Based on the proposed scheme, hexagonal honeycombs of the same mass and varying parameters [ α, η '] were designed and realized via Digital Light Processing (DLP) additive manufacturing. Low-velocity out-of-plane impact tests and dynamic FE calculations were performed to examine the collapse response of geometrically tailored honeycombs and assess their energy absorption characteristics and collapse mechanisms in relation to those observed in conventional (non-tailored) honeycombs of the same mass. The measurements and predictions revealed that the bi-linearly wall-thickness tailored honeycombs consistently outperform their non-tailored counterparts when the impact energy is high, reporting an increase in energy absorption as high as 250%. Such remarkable enhancement in energy absorption is attributed to a transition in the underlying collapse mechanism from global buckling mode to progressive crushing of the cell-walls. We also examined the impact response of honeycombs with periodic variations in cell-wall thickness and found that the latter structures collapse rapidly in an unstable manner, similar to what observed in conventional honeycombs, leading to limited capacity to dissipate the impact energy. With careful selection of the design parameters [α,η′], we experimentally demonstrate that bilinearly wall-thickness tailored honeycombs can exhibit simultaneous improvements in energy absorption and impact resistance, providing new opportunities for expanding the property space of honeycombs and opening the door for a wide range of applications. [Display omitted] [ABSTRACT FROM AUTHOR]

• The representative unit cell (RVE) of CVH is divided into three sub-regions with independent thickness parameters according to the position of the hexagon. • The influence of different thickness distributions on the performance of CVH is investigated to explore the conditions for the emergence of dual-platform features. • Four key design parameters of the whole energy absorption process are extracted, which are derived theoretically based on the stable deformation modes. • A detailed parametric design strategy of the CVH specimen is proposed based on the theoretical analysis, which can regulate the energy absorption curve to the required range. The center-vertex honeycomb (CVH) structure based on the self-similar hierarchical evolution of the hexagonal honeycomb (HH) is introduced in this paper. The CVH structure has stable deformation modes, excellent energy absorption performance, and multi-platform features, and can be applied to multi-stage energy absorption devices with special requirements, such as energy-absorbing components of vehicles and trains. In this study, the multi-stage energy absorption characteristics of CVH under the in-plane quasi-static compression load are investigated numerically and theoretically, which is verified by the experimental test. The representative unit cell (RVE) of CVH is divided into three sub-regions with independent thickness parameters according to the position of the hexagon. The effects of different thickness distributions on the performance of CVH are investigated to explore the conditions for the emergence of dual-platform features. Then, the four key design parameters of the whole energy absorption process are extracted, which are derived theoretically based on the stable deformation modes. Further, a detailed parametric design strategy of the CVH specimen is proposed based on the specific engineering requirements. The design results proved that the proposed design strategy is reliable and accurate, which provides valuable suggestions and guidelines for the regulation of the energy absorption process of relevant structures for specific engineering needs. [Display omitted] [ABSTRACT FROM AUTHOR]

• A finite element-based approach to optimisation of honeycomb-type structures under impact loading for helmet applications is presented. • A novel elastomeric pre-buckled honeycomb structure is optimised to minimise peak linear acceleration and head injury criterion. • Superior single and stabilised multi-impact behaviour is observed for fabricated structures optimised for peak liner acceleration. Finite element simulation was used to analyse the response of an elastomeric pre-buckled honeycomb structure under impact loading, to establish its suitability for use in helmet liners. A finite element-based optimisation was performed using a search algorithm based on a radial basis function. This approach identified optimisation configurations of a pre-buckled honeycomb structure, based on structural bounds subject to impact loading conditions. Furthermore, the influence of objective function, peak acceleration and head injury criterion was analysed with respect to the resultant mechanical behaviour of the structure. Numerical results demonstrate that this class of structure can exceed the performance threshold of a common helmet design standard and minimise the resultant injury index. Experimental testing, facilitated through laser sintering of thermoplastic polyurethane powder, validated the output of the numerical optimisation. When subject to initial impact loading, the fabricated samples satisfied their objective functions. Successive impact loading was performed to assess the performance and degradation. Samples optimised for peak acceleration demonstrated superior performance after stabilisation, relative to their initial response. The culmination of this study establishes a numerical design pathway for future optimisation of candidate structures for head impact protection. Furthermore, the optimised pre-buckled honeycomb structure represents a new class of energy absorbing structure, which can exceed the thresholds prescribed by the design standard. [Display omitted] [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]

• A novel self-similar hierarchical honeycomb is proposed by adding smaller hexagons in the center and the vertex position of the hexagonal honeycomb. • The energy absorption mechanism of the proposed honeycomb is investigated by FEM, which is validated by theoretical results and experimental results. • Two typical plateau stress regions are found under quasi-static compression, and the second plateau stress is over three times higher than the first one. • The presented honeycomb is proved to absorb much more energy than the conventional HH and the vertex-based hierarchical structure with the same masses. In order to enhance the energy absorption capacity of the honeycomb structure, a novel self-similar hierarchical honeycomb is proposed by adding smaller hexagons in the center and the vertex position of the hexagonal honeycomb (HH), and therefore named as center-vertex honeycomb (CVH). An analytical model is built to investigate the in-plane crushing responses of the newly proposed honeycomb, which is in good agreement with the simulation and experimental results. The in-plane quasi-static compression characteristics and energy absorption capabilities of CVH are investigated systematically by finite element method and are compared with that of HH and other hierarchical honeycombs. Two plateau stress regions in the stress–strain curves of CVH are found under the quasi-static compression, and the second plateau stress is over three times higher than the first one. In order to understand the strengthening mechanism clearly, stable unicellular deformation and global modes are revealed. Two typical plateau stress are deduced theoretically based on the collapse modes to achieve performance prediction, which are respectively decided by the hexagonal structures located on both sides and the six vertexes of the representative unit cell. The results show that CVH can absorb much more energy than HH and the vertex-based hierarchical structure with the same masses under quasi-static compression. Furthermore, a parametric study is performed to explore the influence of the impact velocity, the order number, and the wall thickness on the plateau stress, specific energy absorption, and collapse deformation modes of CVH. It can be concluded that CVH is a better choice for energy absorption. The present study provides significant suggestions and guidance for the design-oriented multi-stage energy absorbing reinforced honeycomb structure with special functions. [Display omitted] [ABSTRACT FROM AUTHOR]

• Two crashworthiness indexes of honeycomb sandwich structures are proposed. • The proposed indexes are validated by various honeycomb structures. • The mechanism of crashworthiness indexes is clarified. It is expected to quantitatively determine the crashworthiness of honeycomb sandwich structures in engineering. However, it is challenging due to diverse cell features, hybrid component materials, as well as varied types of impact load. In this study, two dimensionless indexes (i.e., horizontal dent offset displacement per unit depth ϕ and the ratio of horizontal to vertical energy absorption η) are proposed for sandwich structures based on the mechanical response characteristics (deformation and energy absorption) of sandwich structures under low-speed oblique impact. Unlike conventional crashworthiness indexes such as dent depth, specific energy absorption, damage area, etc., the proposed indexes take into account the influence of impact angle (θ) on the mechanical behavior of sandwich structures. Multiple sets of simulation of honeycomb sandwich structures, including conventional hexagonal honeycombs, honeycomb-filled structures and negative Poisson's ratio structures, obliquely impacted (θ varies from 15° ~ 75°) by a rigid body are performed by using the finite element method, whereby the crashworthiness index values of all the sandwich structures are obtained. The index values (ϕ and η) become smaller as the crashworthiness is enhanced (where the wall thickness of the sandwich structure is thickened from 0.02 ~ 0.1 mm). It manifests that the proposed indexes can capture the crashworthiness of sandwich structures under low-speed oblique impact reasonably well. In addition, the proposed indexes can more clearly distinguish the crashworthiness of sandwich structures of different configurations than conventional indexes. The index values (ϕ and η) show that the oblique crashworthiness of the negative Poisson's ratio structure, hexagonal honeycomb, and honeycomb-filled structure becomes stronger in order. [Display omitted] [ABSTRACT FROM AUTHOR]

• The analytical model for Poisson's ratio and effective Young's modulus of the vertex-based hierarchical re-entrant honeycomb structure was built by Timoshenko beam theory first time. • The overlapping effect has a great influence on the relative density of the vertex-based hierarchical re-entrant honeycomb structure, especially for a thick-wall one. • The effective Young's modulus and Poisson's ratio of vertex-based hierarchical re-entrant honeycomb structure can be tailored by adjusting geometrical parameters. • Embedding a re-entrant honeycomb at the vertex of the re-entrant honeycomb is effective for improving its effective Young's modulus. In this study, the mechanical properties of a vertex-based hierarchical re-entrant honeycomb structure (H v) were investigated. Firstly, the overlapping effect of struts was considered in the calculation of the relative density. The results indicate that the overlapping has a great influence on the relative density, especially for a thick-walled structure. Secondly, the theoretical model for evaluating Young's modulus and Poisson's ratio of H v was implemented based on Castigliano's second theorem and Timoshenko beam theory. It shows a good coincidence between the results of the finite element and theoretical models. Thirdly, based on the theoretical model, the variation of the mechanical properties of H v with different geometric parameters was studied. The results indicate that the elastic properties of H v can be designed by appropriately adjusting geometrical parameters. Additionally, the expressions for effective Young's modulus and Poisson's ratio of the conventional re-entrant honeycomb (H c)* were given. H c was compared with H v in terms of the elastic properties by applying the same theory and calculation process. The resultant comparisons suggest that embedding a re-entrant honeycomb at the vertex of H c is an effective way to enhance its elastic modulus and simultaneously maintain the negative Poisson's ratio in a wide range. [Display omitted] [ABSTRACT FROM AUTHOR]