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• 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]

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]

• 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]

· 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]

• 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]

• 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 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]

This paper studies the plastic collapse mechanisms of uniaxially-loaded cylindrical shell-plate periodic honeycombs with identical mass (or relative density) but varying geometric parameters, by series of in-plane and out-of-plane experiments and finite element numerical simulations. The coupled experimental-numerical results show that mechanical properties of the honeycomb can be optimized in all three loading cases, thanks to the complementary changes of the mechanical properties of cylindrical shell and plate as the geometric parameters vary. The work presents a concept to optimize lattice structures by combining different substructures, and can be used in designing new low-density honeycomb structures with desired mechanical requirements but less base materials and weight. [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]

• 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 effects of missing or fractured cell walls on in-plane effective elastic stiffness and initial yield strength of square and triangular cell metal honeycombs are investigated using finite element analysis. Due to the change of localized deformation mode, the in-plane properties of defected honeycombs can differ significantly from those of intact metal honeycombs, depending on cell type and stress state. First, the effect of the size of a statistical volume element of honeycomb cells with randomly removed cell walls is explored by using different numbers of cells with 5% of walls removed, subject to periodic boundary conditions. The size of a representative volume element (statistically homogeneous) is determined for each considered in-plane property. Next, the effective in-plane properties of square cell and triangular cell honeycombs are, respectively, calculated as a function of increasing number density of randomly removed cell walls. Finally, the sensitivities of axial compressive effective properties of these honeycombs to missing cell walls are compared with that of a previously analyzed hexagonal cell honeycomb. The results indicate that some in-plane properties sharply diminish with defect density, while others exhibit more gradual decay. In compression, the effective elastic stiffness and initial yield strength of triangular cell honeycombs are least sensitive to defects among those considered. [Copyright &y& Elsevier]

Finite element simulations were employed to analyse in-plane dynamic crushing of two different hexagonal honeycombs (slenderness ratios L/t=38 and 167). The response of the honeycomb with the smaller slenderness ratio was studied for impact speeds up to 40.0 m/s which corresponds to a nominal strain rate for the specimen of 500 s−1. Total plastically dissipated energy was used to quantify the effects of increasing strain-rate, since other measures showed a strong dependence on details of the finite element model. The simulations revealed a strong increase of total dissipated energy with increasing impact speed for velocities larger than the critical speed for wave trapping, vcr. One reason was a higher percent of cells collapsing in a symmetric crush mode (IV). Another reason for the larger total dissipation at higher crushing speeds was the greater irregularity in the folding pattern that developed. Experimental and calculated global force-time curves were compared for the honeycomb with the larger slenderness ratio at impact speeds 3.0 and 7.2 m/s and a satisfactory agreement was found. At these low impact speeds there was no increase of initial collapse or plateau stresses. A comparison of sequences of deformed mesh plots and high speed photos showed good correlation of the general distribution and modes of crushing. [Copyright &y& Elsevier]

In this paper the dynamics of crush band initiation and wave trapping that result from in-plane impact on a honeycomb are analysed using finite element simulations. The honeycomb structures were loaded in compression at the top surface with a prescribed velocity. Two different boundary conditions were considered; these produced an approximation to a state of uniaxial stress or uniaxial strain at an early state of deformation. The simulations proved that elastic wave propagation had an important effect on crush band initiation, since loading and unloading parts of the compressive wave can reinforce or delay crushing, respectively. Stress enhancement with increasing impact speed is mainly due to translational micro-inertia and not due to micro-rotational inertia. This effect is stronger for uniaxial strain than for uniaxial stress. For the specific case examined here, stress enhancement begins for uniaxial strain at an impact speed of about 1.0 m/s whereas for uniaxial stress it begins at about 10.0 m/s. For the analysed honeycomb the simulation showed for both boundary conditions the existence of a critical impact velocity, so that for impact speeds larger than this critical speed a crush band initiated at the impact surface. For much smaller speeds the location of the initial crush band was determined by the distribution and extent of initial imperfections. In the case of uniaxial stress an analytical estimate of the critical impact speed was derived using the theory of wave trapping. The critical speed depends only on the ratio of the length of the ribbon wall to the length of the thinner inclined wall and the material properties of the constituent material. For the aluminium honeycomb investigated in this paper, wave trapping is predicted to occur for impact speeds greater than 7.6 m/s which is close to the critical speed calculated with the finite element simulations. [Copyright &y& Elsevier]