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Auxetic honeycomb sandwich structures (AHS) composed of a single material generally exhibit comparatively lower energy absorption (EA) and platform stress, as compared to traditional non-auxetic sandwich structures (TNS). To address this limitation, the present study examines the use of aluminum foam (AF) as a filling material in the re-entrant honeycomb sandwich structure (RS). Filling the AHS with AF greatly enhances both the EA and platform stress in comparison to filling the TNS with AF, while the auxetic composite honeycomb sandwich structure effectively addresses interface delamination observed in traditional non-auxetic composite sandwich structures. Subsequently, the positive–negative Poisson's ratio coupling designs are proposed to strengthen the mechanical features of a single honeycomb sandwich structure. The analysis results show that the coupling structure optimizes the mechanical properties by leveraging the high bearing capacity of the hexagonal honeycomb and the great interaction between the re-entrant honeycomb and the filling material. In contrast with traditional non-auxetic sandwich structures, the proposed auxetic composite honeycomb sandwich structures demonstrate superior EA and platform stress performance, suggesting their immense potential for utilization in protective engineering. [ABSTRACT FROM AUTHOR]

Icosahedral B12 serves as a fundamental building block for a variety of boron allotropes and plays a crucial role in enhancing the stability of fullerene-like boron nanoclusters. However, progress in the development of two-dimensional (2D) functional assemblies made from icosahedral B12 has been limited. In this context, we propose a 2D semiconducting boron allotrope (h-B12) using icosahedral B12 as a building block. This structure features a stable honeycomb lattice, with its unit cell comprising two mirror-symmetric icosahedral B12 clusters. The results of first-principles calculations indicate that the band structure exhibits Dirac cones and a relatively high group velocity, similar to graphene. Additionally, it is found to be a material with a negative Poisson's ratio and a relatively low Young's modulus. Finally, our calculations reveal that the zigzag nanoribbon constructed from h-B12 displays prominent edge states at both edges, indicating that this structure represents a potential topological electronic material. Our findings shed light on the design and construction of nano-electronic materials via cluster assembly. [ABSTRACT FROM AUTHOR]

Based on the proposed multi-arc curved edge concave adjustable Poisson's ratio cell, five kinds of sandwich panels with negative Poisson's ratio (NPR) were constructed by changing the in-plane thickness of cells: homogeneous, positive gradient, negative gradient, symmetrical positive gradient, and symmetrical negative gradient. The failure mechanical properties of the sandwich panels under the action of local impact were numerically studied. The influences of impact speed and gradient arrangement modes on the failure mode of the sandwich panels, the punch contact force (PCF) and the energy absorption effect (EAE) were investigated. It is found that the failure behavior of sandwich panels is different under different impact speeds. At the same impact speed, the thickness distribution pattern of the sandwich panel core layer will significantly affect the shock resistance of the panel. The study shows that the EAE of sandwich panels can be effectively enhanced by introducing gradient design method, and the sandwich panels with negative gradient arrangement show the best energy absorption effect. [ABSTRACT FROM AUTHOR]

A theoretical model has been developed to express the longitudinal and transverse piezoelectric effects in ferro/piezoelectrets. This model is an extension of the classic model based on layer-dielectric structures that focuses on the longitudinal piezoelectric effect. The improved model reveals that the relation between the longitudinal piezoelectric d33 coefficient and the transverse piezoelectric d31 coefficient is associated with Poisson's ratio μ13 (or μ31) and Young's moduli Y1 and Y3. The polarity of the two coefficients is opposite for materials with a positive Poisson's ratio as normally observed in conventional piezoelectric materials, and the same for materials with a negative Poisson's ratio, i.e., auxetic materials. The experimental results available in the literature and obtained from ferroelectret metamaterials with a honeycomb cross-sectional structure and two-dimensional (2D) symmetric structure, called 2D ferroelectret metamaterials, designed and prepared in this study reasonably agree with theoretical predictions. This study not only extends the scope of the metamaterials by inducing the concept of ferroelectret metamaterials but also provides a strategy for designing ferroelectrets with designable properties. [ABSTRACT FROM AUTHOR]

This study explores the design and performance of axisymmetric hexachiral honeycombs, utilizing the hexachiral honeycomb framework and axisymmetric design method. Four axisymmetric hexachiral honeycombs with distinct arrangements were developed: left–right symmetry hexachiral honeycomb (LSHH), up–down symmetry hexachiral honeycomb (USHH), central symmetry hexachiral honeycomb (CSHH), and subunits symmetry hexachiral honeycomb (SSHH). The deformation patterns and compression behaviors of these honeycombs were comprehensively examined through experimental and numerical simulations, and comparisons were made with a non-symmetric hexachiral honeycomb (NHH). The results indicate that symmetrically designed honeycombs exhibit a larger mean plateau stress than the asymmetrically designed the NHH during low-velocity impacts. The study further discusses deformation patterns, specific energy absorption, and the negative Poisson's ratio effect across the five honeycombs under different parameters. Notably, symmetrically designed honeycombs demonstrate superior specific energy absorption, and the negative Poisson's ratio effect becomes evident at an impact velocity of 10 m/s. However, the advantages of axisymmetric honeycombs diminish at higher impact velocities of 50 m/s and 100 m/s. The Poisson's ratio effects of symmetric honeycombs weaken with an increase in the circular ligament r of the honeycomb. Additionally, the study identifies that platform stress and SEA increase for honeycombs with horizontal cell numbers greater than 6. [ABSTRACT FROM AUTHOR]

In this study, the graded hierarchical hexagonal honeycomb (GHHH) integrating gradient design and hierarchical design was fabricated using the 3D-printing technique, and its in-plane elastic properties were investigated theoretically, experimentally, and numerically. Theoretical solutions were developed based on the Euler beam theory to predict the effective elastic modulus and Poisson's ratio of GHHH, and theoretical values were in good agreement with the experimental and numerical results. The effect of gradient design and hierarchical design on the in-plane elastic properties of GHHH was also analyzed and compared. Results showed that the hierarchical design has a more significant effect on Poisson's ratio and adjusting the internal forces of GHHH compared with the gradient design. In addition, it was found that GHHH exhibited higher stiffness compared with regular hexagonal honeycomb (RHH), graded hexagonal honeycomb (GHH), and vertex-based hierarchical hexagonal honeycomb (VHHH) under the constraint of the same relative density, respectively. Specifically, the effective elastic modulus of GHHH can be enhanced by 119.82% compared to that of RHH. This research will help to reveal the effect of integrating hierarchical design and gradient design on the in-plane elastic properties of honeycombs. [ABSTRACT FROM AUTHOR]

A fatal weakness in flexible electrodes is mechanical fracture of conductive layer that occurs during repetitive stretching and bending deformation. Thereby, suppression of cracks development is crucially important for maintaining the properties of flexible electronics. Herein, topology optimization and structure design methods are utilized to greatly enhance mechanical properties of the existing island-bridge (I-B) structure. The flexible electrodes, with inner-concave honeycomb negative Poisson's ratio (I-CHNPR) structure and I-B structure, are designed and fabricated via screen-printed process, and conductivity is thoroughly investigated. The research demonstrates that the maximum stretching and bending stress of flexible electrodes with I-CHNPR structure-C are decreased by 30% and 28%, respectively, relative to the I-B structure. Fatigue life is enhanced by 18-fold. In addition, flexible electrode has advantages of better self-recovery and excellent conductivity. The flexible electrode proposed in this article is further applicated to realize the collection of ECG signals which has the advantages of wide application, reusable and high accuracy. The as-obtained flexible electrode with the above advantages is expected to greatly contribute to the emerging research field of flexible electronics. [ABSTRACT FROM AUTHOR]

Previous studies used to take the regular configuration as the element of the cellular structures, then carry out geometric optimization on the initial structures. Nowadays, more and more bionic metamaterial have been studied for their unique properties, such as bionic honeycomb tubular nested structure, bionic sinusoidal honeycomb, butterfly honeycomb, bamboo and beetle forewing thin-walled structures. Here, we report a novel gardenia-shaped honeycomb (GSH) by observing the gardenia from nature. Two valuable mechanical properties within GSH were explored in this study, which can simultaneously provide good deformability and zero Poisson's ratio effect. To understand the mechanical properties of GSH, we show by theoretical, numerical, and experimental methods where is a good agreement. The developed theoretical models for calculating the in-plane elastic modulus are based on Euler-Bernoulli beam theorem and energy principle. The numerical and experimental tensile process at coincident strain were captured to strongly show the deformability of GSH. The findings of this study provide essential guidance for the design of GSH structures with the desired mechanical properties. [ABSTRACT FROM AUTHOR]

Bamboo is an environmentally friendly building structural material. This work investigated the cavity structural characteristics and physical and mechanical properties of honeycomb sandwiches and natural bamboo in the longitudinal direction. The effective elastic parameters of periodically arranged hexagonal bamboo honeycomb cells under in-plane and out-of-plane loads were modeled using analytical and numerical approaches. Then, the effective elastic parameter model of bamboo honeycomb cells was validated by experiments and finite element analysis. The average errors between the calculated and experimental equivalent modulus of elasticity, Poisson's ratio, and shear modulus in the three principal axis directions were 7.43, 4.37, and 8.68%, respectively. The average relativities between the model values of the elastic parameters of the bamboo honeycomb cell and the simulation results in the three directions were 5.46, 5.40, and 6.12%, respectively. The experimental and finite element analysis showed that the constructed effective elastic parameter model of the bamboo honeycomb cell better reflected the state of the bamboo core when subjected to force. This study provides insights for further research on the mechanical properties of bamboo materials and their application in bamboo-based lightweight and high-strength sandwich structures. [ABSTRACT FROM AUTHOR]

Inspired by rotating rigid structures, an auxiliary rotating triangular honeycomb structure (ARTH) is designed in this article. The structure has dual platform stress, which can reduce the initial peak stress generated during collisions, reducing injuries to pedestrians and vehicle occupants. The accuracy of the finite element numerical model is verified by experiments, and a series of researches are carried out. The mechanical properties of the structure at different velocities are studied and the classification diagram of deformation modes is obtained. Under low‐speed impact load, ARTH has two deformation stages and two stress plateau regions, in which the stress of the second plateau is more than twice that of the first plateau. Then, a theoretical model based on plastic dissipation theory predicts the stress platform at different deformation stages under quasi‐static conditions. Parametric analysis shows that increasing wall thickness t can significantly improve the stress platform and energy absorption, but the negative Poisson's ratio effect is weakened. The influence of angle θ on the first stage deformation of ARTH is significant. These studies can provide some references for the design of double‐platform stress and the reduction of initial peak stress of rotating auxiliary structures. [ABSTRACT FROM AUTHOR]

Honeycomb structures have attracted wide attention due to outstanding mechanical properties as promising light material structures. Inspired by nature and artistic design, various honeycombs with different microstructural configurations have been designed for the sake of better mechanical performances and functions. Here, the Miura-origami reentrant honeycomb (MRH) structure integrating reentrant honeycombs (RH) and Miura-origami structures is investigated systematically. Dynamic impact behaviors of the present MRH structure are investigated numerically. The deformation modes and energy absorption capacity of RH and MRH are compared under different impact velocities, including low-velocity, medium-velocity and high-velocity. The results show that the plateau stress and the specific energy absorption(SEA) of MRH is much higher than RH. Moreover, the parametric study indicates that raising the inclined angle will decrease the plateau stress and the absolute value of Poisson'ratio for MRH structures. The specific energy absorption curves increase as the inclined angle of MRH grows up. In addition, the MRH with smaller dihedral angle can absorb much more impact energy and the variation of absorbed energy is proportional to the cell wall thickness of the MRH structure. This work is expected to provide a new thought for designing advanced energy absorption metastructures and achieving superior mechanical performances. [ABSTRACT FROM AUTHOR]

As a promising energy absorbing structure, reentrant honeycomb (RH) structures have been focus of interest in recent years. By reasonably adjusting the geometric configuration of the honeycomb cell, advanced structures with unique mechanical properties and deformation behaviors can be designed flexibly and novely. In this work, inspired by the composite laminates, a novel laminated reentrant honeycomb (LRH) structure is developed by controlling the orientations of RH layers for achieving excellent energy absorption capacity. Mechanical and deformation characteristics of the proposed structures under static and dynamic loadings are investigated experimentally and numerically. By comparing with single-layer RH structure with the same thickness, the results demonstrate that LRH structures have better energy absorption capacity. The deformation modes of RH and LRH structures are also discussed and it is noted that the LRH structure with ±30° honeycomb sublayers shows zero Poisson's ratio effect. It is worth emphasizing that LRH with 0° and 90° sublayers presents similar negative Poisson's ratio effect with RH by analyzing the equivalent Poisson's ratio-strain curves. In addition, it is found that the latter structure has the best energy absorption capacity when the thickness of single-layer 0° RH structure equals to 5 mm. This work provides a new and reliable thought to design the advanced protective structures under compression and impact loadings. [ABSTRACT FROM AUTHOR]

Based on a novel multi-arc concave cell, four types of thickness gradient honeycomb structures with positive gradient, negative gradient, symmetric positive gradient, and symmetric negative gradient are constructed by changing cell wall thickness, and the relative density of the structure is deduced. The in-plane impact dynamics of gradient structure are revealed by numerical method. The deformation collapse mode, the dynamic response curve, the energy absorption effect, and the platform stress of different gradient arrangement and impact velocity are analyzed. It is found that gradient arrangement and impact velocity have significant effects on the impact properties of the thickness gradient honeycomb structures. When the impact velocity is low, the structure shows laminar shrinkage deformation, but this phenomenon will gradually disappear with the increase of impact velocity. The results show that the energy absorption capacity of the negative gradient structure is the best under different impact velocities. The platform stress is greatly affected by the impact velocity and less affected by the gradient arrangement. [ABSTRACT FROM AUTHOR]

This paper presents a novel rhombic star-shaped honeycomb (RSSH) configuration with tunable Poisson's ratio and elastic modulus, and an RSSH with the U-shaped ligaments (URSSH) configuration is generated to analyze the effect of the curved ligaments on the elastic properties of RSSH. Cellular structure of RSSH combines with a rhombic and an improved star-shaped geometry, which can also be subdivided into flexible segments and rigid segments. In-plane elastic properties of the RSSH cell, including Poisson's ratio and elastic modulus, are both derived by analytical model based on flexibility modeling method and Castigliano's second theorem. Based on the guidance of theoretical model, quasi-static tensile experiments and finite element simulation of RSSH and URSSH specimens are carried out with different Poisson's ratio. The experimental results are in good agreement with the theoretical predictions and finite element analysis results. Length of cellular ligaments Lt1, dt have linear relationship with mechanical properties of the RSSH cell under constant angle θ1 and make the cellular configurations with different Poisson's ratio more obtainable. The effect of the symmetry of the flexible segments on the cellular mechanical properties is also analyzed through theoretical prediction. The introduction of asymmetry can bring wider design space of RSSH mechanical properties, especially Poisson's ratio. This work demonstrates the promising potential for applying RSSH configurations in 2D morphing structures with tunable auxetic behaviors. [ABSTRACT FROM AUTHOR]

To realize the one‐dimensional deformation of morphing wings, zero Poisson's ratio (ZPR) honeycomb metamaterials have become a popular research topic due to their lightweight, low in‐plane modulus, and high out‐of‐plane strength. A ZPR honeycomb metamaterial is designed and prepared from short‐cut carbon fiber‐reinforced polyetheretherketone (CF/PEEK) by a 3D printer. The mechanical properties of ZPR honeycomb metamaterials were tested to determine their tensile and bending stiffness. The results show that the metamaterial can achieve 62.3% ± 3.3% in‐plane elastic deformation after optimized structure design. At the same time, metamaterial has a certain bending resistance to keep the airfoil from normal buckling deformation. Moreover, a new test method for evaluating the cycle deformation behavior of flexible morphing wings is proposed. The high‐speed cyclic tension‐compression test showed that H22‐t0.6‐CT has the best stability, which may be related to its lower porosity (2.15% ± 0.12%). These results indicate that ZPR honeycomb metamaterials have great application prospects in the field of morphing wings. Highlights: The printed CF/PEEK wire is treated as a transversely isotropic material.ZPR honeycomb metamaterial allows for more than 50% in‐plane deformation.A new test method to evaluate the cyclic deformation behavior. [ABSTRACT FROM AUTHOR]

In this article, the non‐linear free vibration behavior of sandwich composite panels with sinusoidal corrugations is examined. These panels consist of a top and bottom skin made of a graphene‐reinforced composite, with an auxetic honeycomb core having negative Poisson's ratio. The non‐linear kinematic field is based on Kant's higher‐order shear‐deformation theory and the Green‐strain, which incorporates all the higher‐order terms. By implementing the Hamilton principle, the non‐linear governing equations are affirmed and solved further through 2D‐isoparametric finite element approximations via Lagrangian elements in conjunction with Picard's successive iterative scheme. The comparison and validation tests demonstrate the correctness of the present model. The established sandwich model is further employed for various parametric conditions by varying the core‐to‐face sheet thickness, auxetic honeycomb properties, graphene volume fraction, shell configurations, temperature, and support conditions. These numerous results exemplify the non‐linear frequencies at small‐to‐large amplitudes for the sandwich shell structures and are discussed in detail. In addition, a multi‐objective parametric optimization is conducted using the response surface method to investigate the optimal values of the corrugated auxetic honeycomb shell panel's parameters, resulting maximum frequency. Highlights: Non‐linear vibration of corrugated sandwich shell panel.Graphene reinforced skins and honeycomb auxetic core.Kant's higher‐order shear‐deformation theory and Green‐Lagrange non‐linearity.Hamilton principle and Picard's successive iterative scheme.Multi‐objective parametric optimization and prediction using response surface methodology. [ABSTRACT FROM AUTHOR]

Lattice structures nowadays have gained a peak in research. Inspired by the honeycomb structure and fishbone, this study investigated lattice structures that can provide auxetic behavior and store maximum energy absorption during deformation mode. From that, the study involved designing and producing different modified lattices based on the honeycomb's structure and the fishbone's perspective. The specimens were 3D printed within fused filament fabrication techniques within the additive manufacturing platform of Euromed University of Fes. The conception, production, mechanical testing, and simulation have been employed to get optimum data analysis of the mechanical properties of the designed structures. The results observed under quasi-dynamic compression did not show significant densification behavior; but, the auxetic behavior was seen in all structures, while some suddenly collapsed. The experimental and numerical analysis demonstrated similar deformation behavior and strong agreement in their respective results. Nevertheless, some discrepancies in mechanical values were observed, with a relative percentage error of approximately 1% for both methods. Consequently, owing to the enhanced energy absorption observed in the V2 and V3 structures, it is evident that these modifications hold promise for optimizing the performance of these metamaterials in various practical applications. [ABSTRACT FROM AUTHOR]

This analysis investigated the impact wave response and propagation on a composite sandwich shell when subjected to a low-velocity external shock, considering hygrothermal effects. The sandwich shell was crafted using face layers composed of functional gradient metal–ceramic matrix material and a core layer reinforced with negative Poisson's honeycomb. The honeycomb layer consisted of a combination of viscoelastic polymer material and elastic material. The equivalent parameters for the functional gradient material in the face layers were determined using the Mori–Tanaka and Voigt models, and the parameters for the negative Poisson's ratio honeycomb reinforcement core layer were obtained through Gibson's unit cell model. Parameters relevant to a low-velocity impact were derived using a modified Hertz contact law. The internal deformations, strains, and stress of the composite sandwich shell were described based on the higher-order shear deformation theory. The dynamic equilibrium equations were established using Hamilton's principle, and the Galerkin method along with the Newmark direct integration scheme was employed to calculate the shell's response to impact. The validity of the analysis was confirmed through a comparison with published literature. This investigation showed that a multilayer negative Poisson's ratio viscoelastic polymer material honeycomb-cored structure can dissipate impact wave energy swiftly and suppress shock effectively. [ABSTRACT FROM AUTHOR]

Negative Poisson's ratio as the anomalous characteristic generally exists in artificial architectures, such as re‐entrant and honeycomb structures. The structures with negative Poisson's ratio have attracted intensive attention due to their unique auxetic effect and many promising applications in shear‐resistant and energy absorption fields. However, experimental observation of negative Poisson's ratio in natural materials barely happens, although various 2D layered materials are predicted in theory. Herein, the anisotropic Raman response and the intrinsic intralayer negative Poisson's ratio of 2D natural black arsenic (b‐As) via strain engineering strategy are reported. The results are evident by the detailed Raman spectrum of b‐As under uniaxial strain together with density functional theory calculations. It is found that b‐As is softer along the armchair than zigzag direction. The anisotropic mechanical features and van der Waals interactions play essential roles in strain‐dependent Raman shifts and negative Poisson's ratio in the natural b‐As along zigzag direction. This work may shed a light on the mechanical properties and potential applications of 2D puckered materials. [ABSTRACT FROM AUTHOR]

In this research, free curling property of the over‐expanded honeycomb (OH) with zero Poisson's ratio was utilized to design and manufacture curved carbon fiber‐reinforced composite (CFRC) sandwich beams by hot compression molding technique and co‐curing process. Three‐point bending experiments were conducted to reveal the failure mechanism of these OH‐based curved sandwich beams with various curvatures. The results reveal that in this research no matter what the curvature is, the shearing fracture of the OH core controls the initial failure of the curved structure, which is followed by upper skin fracture, lower skin delamination and fracture. With the increase of curvature, the ultimate bearing capacity and flexural rigidity of the curved beams will increase. No debonding was observed in the experiments. Highlights: Curved sandwich beams with zero‐Poisson's ratio honeycomb‐core was designed.Deformation process from arc, flattening to anti‐arc was revealed by testing.Strength of curved sandwich beams depends on shear strength of the honeycomb.Beams with smaller curvature have greater bearing capacity and stiffness. [ABSTRACT FROM AUTHOR]

• Impact response of stiffened sandwich FGPM doubly-curved shell with re-entrant honeycomb auxetic core is studied. • The interaction between the impactor and shell utilizes equivalent spring-mass (SM) model consisting two-degrees-of freedom. • The facesheets are made from FGPM and the shell structure is modeled by first order shear deformation theory. • The impact performance of re-entrant honeycomb auxetic core is compared with regular hexagonal honeycomb core. Owing to unique deformation behavior and high capacity of energy absorption, auxetic structures have garnered significant research attention. To reveal the energy-absorbing properties of the auxetic structure, the impact response of stiffened sandwich functionally graded porous materials (FGPM) doubly-curved shell with re-entrant honeycomb auxetic core is studied by the established analytical model in the present work. The material properties in the thickness direction of FGPM face sheets are adjusted according to the volume fraction of constituents by power law and exponential law, while the core layer is made of the re-entrant honeycomb auxetic core with negative Poisson's ratio. On the basis of the Hertz theory for elastic impacts and the first-order shear deformation theory (FSDT), an analytical model is developed to study its impact phenomenon. Equations of motion are derived using Hamilton's principle, which are further solved analytically using Navier's technique of assuming unknown variables in the double trigonometric series. The time-dependent contact force is obtained by applying the spring-mass (SM) model consisting two-degrees-of freedom. Afterward, the transverse central displacements of the stiffened sandwich FGPM doubly-curved shell are calculated by adopting the Duhamel integration. The impact force and transverse displacements are compared with the previously published results, indicating that the theoretical results agree with the previously published results. Parametric analyses have been carried out to investigate the effect of variation of various parameters such as volume fraction exponents, radii of principal curvatures, porosity volume fraction, core layer inclined angle on the impact response of the sandwich shell. Additionally, the results show that compared with the traditional hexagonal honeycomb core type, the stiffened sandwich FGPM doubly-curved shell with re-entrant honeycomb core type has significant advantages in impact energy absorption. This work may provide an extensive reference and valuable guidance in the impact design and application of auxetic sandwich shell structures. [ABSTRACT FROM AUTHOR]

The conventional star-shaped honeycomb (CSSH) structure is inherently rich in mechanical properties. Based on the CSSH structure, the Poisson's ratio and Young's modulus can be improved by adding the tip re-entrant angle (ISSH). In this paper, a new concave four-arc honeycomb (CFAH) structure is proposed by designing the straight rod as a curved rod and retaining the tip re-entrant angle from the ISSH structure. The Young's modulus, specific stiffness and Poisson's ratio of CFAH structures are derived from Castigliano's second theorem and Moore's theorem. The theoretical results show good agreement with the numerical and experimental results. The results show that the normalized effective specific stiffness and normalized effective Young's modulus of the CFAH structure are further improved by about 12.95% and 16.86%, respectively, compared with the ISSH structure, and more significant auxiliary effects are obtained. CFAH structures show good promise in aerospace, construction and other applications due to their enhanced mechanical property. Meanwhile, the present work provides guidance for the study of concave four-arc honeycomb structures. [ABSTRACT FROM AUTHOR]

There has been significant research focused on the development of stretchable materials that can provide a large area with minimal material usage for use in solar cells and displays. However, most materials exhibit perpendicular shrinkage when stretched, which is particularly problematic for polymer-based substrates commonly used in stretchable devices. To address this issue, biaxial strain-controlled substrates have been proposed as a solution to increase device efficiency and conserve material resources. In this study, we present the design and fabrication of a biaxial strain-controlled substrate with a re-entrant honeycomb structure and a negative Poisson's ratio. Using a precisely machined mold with a shape error of less than 0.15%, we successfully fabricated polydimethylsiloxane substrates with a 500 μm thick re-entrant honeycomb structure, resulting in a 19.1% reduction in perpendicular shrinkage. This improvement translates to a potential increase in device efficiency by 9.44% and an 8.60% reduction in material usage for substrate fabrication. We demonstrate that this design and manufacturing method can be applied to the fabrication of efficient stretchable devices, such as solar cells and displays. [ABSTRACT FROM AUTHOR]

Here, hexagonal and triangular lattices are layered and merged into a re-entrant honeycomb to replace each cell wall of the re-entrant honeycomb. In order to study the crushing behavior of the new variable-angle-variable-substructure-number-gradient honeycomb, a finite element analysis of in-plane and out-of-plane crushing was carried out. The effects of different gradient parameters on the deformation mode and extrusion response were discussed, respectively. The results show that different grading parameters have different effects on the crushing behavior of honeycombs for in-plane and out-of-plane crushing. Compared with out-of-plane crushing, the influence of the hierarchical structure on the in-plane crushing deformation mode and the increase in platform stress are much larger. Compared with the ordinary honeycombs, changing the substructure angle does not necessarily improve the platform stress of the honeycomb. From the perspective of platform stress, the layered structure has different effects on the improvement of honeycomb energy absorption; the maximum platform stress of the honeycomb is increased. [ABSTRACT FROM AUTHOR]

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Asymmetric free vibration analysis of composite cylindrical shells with a honeycomb core layer and adjustable Poisson's ratio is performed analytically in this study. The equations of motion which are a system of coupled partial differential equations are extracted using Hamilton's principle by employing the first-order shear deformation theory and they are solved analytically. To study the sensitivity of the results to the different parameters of the honeycomb structure, geometrical parameters, and boundary conditions, a parametric study is presented. It is concluded that for the auxetic composite shell with a negative Poisson's ratio, by decreasing the Poisson ratio, the frequency decreases. Also, it is shown that by employing the composite shells the weight decreases significantly, while the asymmetric frequency will not change remarkably. By adjusting the Poisson ratio, the frequency variations are studied for a composite shell with a honeycomb core layer. The results are compared with the finite element method and some other references. [ABSTRACT FROM AUTHOR]

By utilizing 3D printing technology, experimental three-point bending (TPB) tests, and finite element analysis, six honeycomb structures with a variety of overall Poisson's ratios (PR) are studied and compared in terms of bending properties and failure mechanisms. Four novel honeycombs that are designed by hybridizing hexagonal and re-entrant units outperform benchmark conventional honeycombs in terms of load-carrying capacity. Architected hybrid geometry honeycombs with zero PR show excellent specific energy absorption capability in comparison to benchmark honeycombs, absorbing approximately 136.9% and 475.1% more energy under TPB. 3D-printed honeycombs consisting of hexagonal units face layer separation damage mode under bending, while honeycombs with re-entrant cells in their lattice fail with joint shear due to the angle of their struts towards loadings. Designing honeycombs with a hybrid geometry lattice can enhance the load-carrying capacity, specific energy absorption, flexibility, and flexural modulus of the structure under bending. Due to their superior performance, the proposed architected hybrid geometry honeycombs with various Poisson's ratios own promising applications in automotive, protective, and construction industries. [ABSTRACT FROM AUTHOR]

As an alternative to the conventional concave hexagonal honeycomb structure (CHHS), a negative Poisson's ratio honeycomb structure with power function curve (NHPC) was devised. The relationship between the power function exponent (PFE) and normalized power function coefficient (NPFC) of honeycomb structure and its equivalent Poisson's ratio (EPR) was explored to identify the range of variables required for the negative Poisson's ratio effect. To investigate the in-plane mechanical properties and energy absorption characteristics of NHPC, the deformation mode, dynamic response, and energy absorption characteristics under various impact velocities were studied by constructing an in-plane impact simulation model. The results showed that NHPC obviously exhibited a negative Poisson's ratio effect on medium and low impact velocities, and the deformation was primarily uniform. As the NPFC increased, the honeycomb structure was less prone to stress concentration, while the peak crushing force (PCF) and the specific energy absorption (SEA) declined and the plateau stress increased. A multi-objective optimization experiment was operated with low PCF and high SEA as the targets within the range of design variables in order to generate the optimal NHPC. According to the experimental findings, the improved NHPC showed a 25.48 % reduction in PCF and a 19.29 % increase in SEA. This paper provides theoretical recommendations for improving the energy absorption and structural optimization of the honeycomb structure. [ABSTRACT FROM AUTHOR]

Apart from the inherent anomalous behaviour under tensile and compressive structures, auxetic structures have shown improved energy absorption characteristics that are of prime interest to various fields of study. This is further exemplified by additive manufacturing (AM) techniques and polymer composites to tailor the shape, geometry and form of these structures. Consequently, this paper aims to characterise the in-plane compressive behaviour and negative Poisson's ratio (NPR) of the most prominent auxetic structures fabricated additively used polymer nanocomposite materials. The study incorporates the use of glycol-modified polyethylene terephthalate (PETG) and nanocomposites of PETG filled with organically modified montmorillonite (OMMT) nanoclay particles to produce auxetic structures fabricated through fused filament fabrication (FFF). Different structures such as hexagonal re-entrant honeycomb structures, peanut-shaped honeycombs, chiral honeycomb structures and missing rib structures are characterised for their compressive performance through experimental approaches involving mechanical testing and digital image correlation (DIC). Different parameters such as the peak crushing strength, average crushing strength, NPR, specific energy absorption (SEA), and crush force efficiency (CFE) of these structures are evaluated at different strain rates/loading rates for varying concentrations of nanoclay and PETG. It is observed that higher loadings of nanoclay particles lower the compressive strength of the structures. Additionally, the NPR decreases with increasing strain rates and is also influenced by the composition and the resultant stiffness. Moreover, the geometrical parameters of the structure largely influence its strain energy absorption. The results have shown that such material-structure combinations can produce structures of high-performance capabilities suitable for aerospace applications. [ABSTRACT FROM AUTHOR]

Honeycomb core sandwich may suffer from face/core debonding. Candidate debond fracture test specimens such as End-Notch Flexure (ENF) and Mixed Mode Bending (MMB) contain unbonded regions of the sandwich where the core is required to carry in-plane com-pressive load. In-plane modulus and compressive strength of honeycomb core are not pro-vided by core producers and must be estimated from unit cell models assuming perfect hexagonal cells. In this study it is shown that geometrical imperfections, such as deviations in the angle between cell walls and curved cell walls have a strong influence on modulus and strength because of deviations from transverse isotropy. A range of Nomex honeycomb cores were tested under in-plane compression. Modulus and strength ratios (L/W) were found to vary from 0.3 to 3.24 and 0.96 to 1.8, respectively. Analysis based on unit cell models verified that deviations of the inclined cell wall angle, θ, from 30 ◦ is a major cause for orthotropy. Rounded corners and curved walls were analyzed using finite element analysis. Both principal elastic moduli of the core (E L and E W ) were reduced by the curvature while the Poisson's ratios remained largely unaffected. Implications of the results for design of MMB and ENF fracture test specimens are discussed. [ABSTRACT FROM AUTHOR]

To enhance the load‐bearing capacity and energy absorption capacity of the honeycomb, three kinds of star‐rhombus honeycombs (SRHs) are proposed by adding rhombic parts to the traditional star‐shaped honeycomb (TSH). The quasi‐static crushing responses of SRHs, including deformation mechanism, crushing stress, specific energy absorption (SEA), and Poisson's ratio, are studied based on the finite‐element (FE) method. The introduction of rhombic parts increases the number of plastic hinges, resulting in significantly higher crushing stress and SEA of the SRHs than that of the TSH. Among the SRHs, SRH‐A has the largest energy absorption, and the SEA value of SRH‐A is 98.2% higher than TSH. Then, parametric studies including wall thickness, cell wall angle, and spacing length between the vertices of the star‐shaped part and the rhombic part are carried out. The wall thickness and cell wall angle have the greatest influence on the crushing response of SRHs. Crushing stress and Poisson's ratio of SRHs can be adjusted by changing the wall thickness of the rhombic part. The configurations and geometric parameters of the rhombic part determine the Poisson's ratio of SRHs. This study provides effective guidance for designing star‐shaped honeycombs with enhanced load‐bearing capacity and energy absorption capacity. [ABSTRACT FROM AUTHOR]

This paper reports a new annular honeycomb that shows tunable Poisson's ratio. The presented honeycombs can provide both the in-plane negative Poisson's ratio (NPR) and in-plane zero Poisson's ratio (ZPR) while the shapes of the honeycomb core change. The developed honeycomb core is constructed by an annulus with four ligaments distributed bi-axial symmetrically, which shows great diversity of mechanical properties. The developed theoretical models of the in-plane elasticity are based on Castigliano's Second Theorem and energy principle. Two parameters were used to describe the deformation mechanisms of the unit cell concisely. The effect of two parameters on the Poisson's ratio and Young's modulus was investigated. The Young's modulus derived from the Finite Element (FE) analysis all have an good agreement with that derived from theoretical results, and the experiments were carried out to confirm the validity of them convincingly. [ABSTRACT FROM AUTHOR]

This work develops a novel design method for the actively deformable honeycomb structure to realize the variable thickness leading-edge wing. Firstly, the classical Gibson theory is extended to be applicable for the non-regular hexagonal honeycomb single-cell with the positive Poisson's ratio and the concave hexagonal honeycomb single-cell with the negative Poisson's ratio. The equivalent mechanical properties of the above two types of single-cells are deduced. Then, the concept of the deformation unit composed of positive and negative Poisson's ratio honeycomb multi-cells is proposed. The shape memory alloy is assigned as an actuator to produce the in-plane incompatible deformation which excites the out-of-plane bending of the deformation unit. The relationship between the in-plane driving displacement and the bending angle of the deformation unit is investigated. The segmented two-layered honeycomb-core plate composed of positive and negative Poisson's ratio honeycomb layers is constructed using deformation units. Finally, the initial configuration of the leading-edge is simulated by the segmented honeycomb-core plate. The driving displacements required to be imposed to each deformation unit are determined according to the target shape of the leading-edge. The proposed method is validated by changing the leading-edge from the blunt shape to the sharp shape, using finite element simulations. [ABSTRACT FROM AUTHOR]

This study aims to improve the impact protection performance of composite structures by combining a honeycomb core with negative Poisson's ratio and graphene platelets reinforced (GPR) face sheets. The paper investigates the nonlinear repeated low-velocity impact responses of auxetic honeycomb composite plates, taking into account loading-unloading-reloading processes. Effective material properties of the auxetic honeycomb core and GPR face sheets are obtained by using the proposed modified Gibson function and Halpin-Tsai model. Then, taking into account geometric nonlinearity, the nonlinear equations of motion for the system were derived by Hamilton's principle. Afterward, the time-varying contact force between the composite plate and a spherical impactor is defined by the modified nonlinear Hertz contact theory. The Galerkin method and variable-step Runge-Kutta algorithm are selected to obtain nonlinear impact responses. The proposed methods are verified by finite element simulation and experiment. Finally, the study evaluates the effects of key parameters on the nonlinear repeated low-velocity impact responses. [ABSTRACT FROM AUTHOR]

The nonlinear, in-plane mechanics of a thin-walled honeycomb with zero Poisson's ratio under large deformation is investigated in this paper. A theoretical method for calculating in-plane tensile modulus, modified factors of linear constitutive relations of the honeycomb structures with zero Poisson's ratio is proposed based on the theory of Euler-Bernoulli beam and the bending theory of beam in large deflection, and a finite element simulation is given to validate. In addition, parametric analysis for revealing the impacts of geometrical configurations and material parameters on in-plane mechanical properties of the honeycombs have been studied systematically. These findings suggest that geometric and/or material parameters provide different contributions to the effective mechanical properties and lead to a separate design for the in-plane mechanical properties. After that, the effects of geometric and/or material nonlinearities on mechanical properties of the honeycomb structures with zero Poisson's ratio are revealed by considering the dimensionless tangent stiffness of the honeycombs. [ABSTRACT FROM AUTHOR]

Honeycomb structures with zero Poisson's ratio show promising potential for application in variable-sweep wing aircraft. The shear properties of these honeycomb structures serve as a crucial indicator of their morphing capacity. This paper derives the linear and non-linear shear properties of a honeycomb structure with zero Poisson's ratio. A modified factor is introduced to establish a relationship between the linear and non-linear shear modulus of the honeycomb structure, simplifying the calculation method of the non-linear shear modulus. The validity of theoretical predictions is then confirmed using the finite element method Furthermore, the influences of the geometric parameters on the shear properties of the honeycomb structure with zero Poisson's ratio are investigated, highlighting the varying contributions of these cell geometric parameters to the shear properties. [ABSTRACT FROM AUTHOR]

An improved star-shaped honeycomb (ISSH) is a kind of honeycomb structure with excellent performance. The main objective of this study was to provide some ideas for the optimization of the ISSH structure in ships. As a result, 2D-ISSH specimens were fabricated using 3D printing technology, and a quasistatic compression test was carried out to investigate the deformation mode and mechanical properties. The experimental results showed that the 2D-ISSH structure exhibited "V"-shaped and "-"-shaped deformation patterns with a double-platform stress stage. To further utilize the excellent performance of the structure and obtain a better negative Poisson's ratio effect and broader application, based on the properties of the 2D-ISSH specimen, a 3D-ISSH structure was proposed and a finite element simulation was carried out. The simulation results of the 3D-ISSH structure showed different deformation patterns, including "X"- shaped and "-"-shaped patterns. According to the deformation mechanism of typical cells, the stress formula for the 3D-ISSH double platform was derived, and the theoretical results agreed well with the numerical results. The effects of the structural design, materials, and dimensions on the mechanical properties, such as the energy absorption and negative Poisson's ratio, of the ISSH and similar structures were explored. The combined performance of various honeycombs was evaluated from multiple perspectives. [ABSTRACT FROM AUTHOR]

To investigate the effect of nodal configuration on the mechanical properties of hexachiral honeycombs, three specimens, namely, a standard honeycomb, a thickened-node honeycomb, and a filled-node honeycomb, were prepared using 3D-printing technology. Several quasi-static compression tests were performed, which revealed that nodal reinforcement can inhibit nodal aberrations during ligament winding, thus facilitating the "rotational" mechanism and improving the negative Poisson's ratio properties of the honeycomb. Experiments performed using the finite element method showed that nodal reinforcement mainly played a role in the stage of stress rise, and the role of nodal filling was more significant than that of nodal thickening. Low-strain standard honeycombs presented the highest specific absorption energy. However, the specific absorption energy of the filled-node honeycomb and the thickened-node honeycomb exceeded that of the standard honeycomb at a strain of 0.71. The conclusions presented herein can aid in the optimal design of honeycombs and contribute to the design of protective structures. [ABSTRACT FROM AUTHOR]

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This study proposes to investigate the crushing performance of auxetic honeycombs by combining liquid and solid phase materials in one structure. The multiphase structures were produced by injecting a liquid Gallium metal into the hierarchical voids of the proposed metamaterials and tested at different temperatures (22 and 35 0C), where the melting temperature of Gallium metal is 29.4 0C. The deformation mechanism, compressive strength, absorbed energy, and Poisson's ratio (PR) of the samples was compared at different strains and at different temperatures. Results show that multi-material samples with Gallium metal lead to a progressive deformation mechanism and stabilize the fracture mechanism; however, they only exhibit larger compressive strength in a few cases. In addition, the effects of the phase change of Gallium from solid to liquid when the temperature increase from 22 0C to 35 0C stand out in the percent change of mechanical response. Overall, the presented samples in this work can be recommended to manipulate the collapse mechanism with a multi-material approach of liquid and solid constituents. [ABSTRACT FROM AUTHOR]

Auxetic metamaterials with two components exhibit a wide variety of potential engineering applications due to their exotic mechanical properties. In this work, a novel straight-arc coupled structure (SACS) is designed by introducing a circular arc structure to a classical re-entrant structure. This work aims to explore the linear and geometrical nonlinear mechanical of SACS at large strains. According to Castigliano's second theorem, the in-plane linear theoretical model is established to obtain equivalent Poisson's ratio and elastic modulus. A geometrical nonlinear model is further established based on large deflection theory and chain algorithm. The finite element method is used to verify the prediction of the theoretical solution, and linear and nonlinear mechanical properties of the SACS are studied by numerical simulation. The influence of geometric parameter re-entrant angle and arc radius on the mechanical properties of the SACS is investigated to compare the linear and nonlinear mechanical properties. The linear numerical simulation of SACS with two transverse ribs (SACS-TR) and classical re-entrant honeycomb structure with two transverse ribs (CRS-TR) is carried out to analyze the in-plane elastic properties. These results demonstrate that considering the geometric nonlinear model can predict the actual structural deformation more accurately, which is verified by the quasi-static compression experiment results at large strains. The SACS design can enhance the auxetic effect and structure Young's moduli under the same dimension. [ABSTRACT FROM AUTHOR]

This paper analyzes and calculates the mechanical properties of composite tape spring structures during folding and bending and establishes a non-linear control equation for the folding and bending of composite laminate tape spring structures. Accurate expressions for folding and bending displacements are obtained. The influence of the cross-section's central angle and the composite tape spring's ply thickness on their mechanical properties are analyzed. Finite element numerical analysis is performed on [−45 45]s laminated composite tape springs, and the correctness of the theoretical derivation is proved by comparing the curvature radius-bending moment curve. Based on previous research, the mechanical properties of different tape spring materials and structures are compared, further studying the lightweight design of space deployment mechanisms. The results show that the steady-state bending moment performance of composite tape springs is excellent, with a 162.1% improvement in steady-state bending moment performance per unit mass compared to traditional metallic tape springs. Additionally, the critical bending moment performance of negative Poisson ratio honeycomb structure tape springs is also excellent, with a 62.3% improvement in steady-state bending moment performance per unit mass compared to traditional metallic tape springs. [ABSTRACT FROM AUTHOR]

Auxetic honeycomb has unique mechanical properties such as good energy absorption capacity, tensile strength and fracture toughness, etc. Therefore, honeycomb with a negative Poisson's ratio is used widely in medical, biological, aerospace and other fields. This honeycomb has large deformations in energy absorption and vibration reduction. It is very important to study the nonlinear constitutive of the honeycomb structure. Therefore, this paper establishes the nonlinear constitutive relationship of the auxetic honeycomb structure under large deformations. This constitutive relation includes the in-plane stress, in-plane strain, Young's modulus and Poisson's ratio of the negative Poisson's ratio honeycomb. The finite element model of the negative Poisson's ratio honeycomb cells is established, and the calculated results of finite element model are compared with that of the theoretical calculation results. On this basis, the influence of the geometric parameters on the mechanical properties of the structure is studied. The results of this paper will provide a theoretical basis for the further study of the auxetic honeycomb sandwich structure and provide a basis for the engineering application of honeycomb structures. [ABSTRACT FROM AUTHOR]

This article investigates the static analysis of functionally graded electromagnetic nanocomposite sandwich plates reinforced with graphene platelets (GPLs) under hygrothermal loads. The upper and lower layers of nanocomposite face sheets are made of piezoelectromagnetic material with randomly oriented and uniformly disseminated or functionally graded (FG) GPLs throughout the thickness of the layers, while the core layer is made of honeycomb structures. The effective Young's modulus of the face sheets of the sandwich plate is derived with the aid of the Halpin–Tsai model. While the rule of mixtures is incorporated to compute Poisson's ratio and electric-magnetic characteristics of the sandwich plate's upper and lower layers. The governing equations are obtained by a refined quasi-3-D plate theory, with regard to the shear deformation as well as the thickness stretching effect, together with the principle of virtual work. Impacts of the various parameters on the displacements and stresses such as temperature, moisture, GPLs weight fraction, external electric voltage, external magnetic potential, core thickness, geometric shape parameters of plates, and GPLs distribution patterns are all illustrated in detail. From the parameterized studies, it is significant to recognize that the existence of the honeycomb core causes the plate to be more resistant to the thermal condition and the external electric voltage because of the weak electricity and thermal conductivity of the honeycomb cells. Consequently, the central deflection decreases with increasing the thickness of the honeycomb core. Moreover, with varying the external electric and magnetic potentials, the deflection behavior of the sandwich structures can be managed; raising the electric and magnetic parameters contribute to an increment and decrement in the deflection, respectively. [ABSTRACT FROM AUTHOR]

The innovative design of microstructure topology is of great significance to improve the energy absorption performance of honeycombs. In this paper, by embedding a hexagonal substructure in each inclined wall of the traditional reentrant (RE) honeycomb, a novel auxetic honeycomb, called reentrant combined-wall (RCW) honeycomb, is developed for improving energy absorption. Combining the experimental methods, numerical simulations, and analytical analyses, we systematically studied the in-plane quasi-static behaviors of the proposed honeycomb structure. It can be found that the deformation of the RCW honeycomb has a transitional stage, which makes a significant stress enhancement. During the crushing process, the Poisson's ratio of the RCW honeycomb keeps negative and is lower than that of the RE honeycomb. Besides, numerical and analytical analyses show that the stress-strain response of the RCW honeycomb has a good designability. Further, the analysis of specific energy absorption (SEA) is also performed, in which the RCW honeycomb shows a significant superiority over the RE honeycomb, with the SEA value almost twice that of the latter. Therefore, it can be concluded that the proposed novel structure has tangible improvements in the crushing strength, auxetic performance, and energy absorption, which deserves more attention in future work. [ABSTRACT FROM AUTHOR]

The tape spring is a crucial component used in the deployment mechanism of spacecraft, and the lightweight design of the deployment mechanism is currently one of the critical issues that need to be addressed. This paper explores the substitution effect of two different negative Poisson's ratio honeycomb-corrugated spring structures for use in space-deployable structures. Theoretical and finite element methods demonstrated that the negative Poisson's ratio honeycomb structure could be equivalent to an orthotropic structure. The cylindrical shell bending theory was adopted, taking into account the nonlinearity of the geometric equation, the influence of cross-sectional deformation and cross-sectional position on the internal force expression, and the influence of the geometric equation to derive expressions for the bending moment and curvature radius during the folding and bending process. Numerical methods were used for comparative analysis. The NSGA-II algorithm optimized the geometric parameters of the negative Poisson's ratio honeycomb, resulting in the optimal solution under given constraints. The results showed that the Auxetic re-entrant honeycomb structure performed better in bending moment capacity than the Star-shaped honeycomb, and the bending moment capacity of the Auxetic re-entrant honeycomb structure per unit mass was superior to that of the traditional tape spring. [ABSTRACT FROM AUTHOR]

With the increase of demands for anti-collision performance in many fields, the negative Poisson's ratio structure has attracted the attention of researchers due to its light weight and high shear stiffness. Therefore, a new negative Poisson's ratio (NPR) structure named three-beam star honeycomb (TBSH) is proposed based on the classical star honeycomb (CSH). The stress equation of TBSH is derived by energy method, and its deformation characteristics and mechanical properties are studied. The results show that the structural deformation modes are different under different impact velocities, and TBSH has more obvious NPR effect. In addition, the influence of geometrical parameters on energy absorption of structures is also investigated. Finally, the thickness gradient is introduced into this structure, and the thickness gradient is optimized by multi-island genetic algorithm (MIGA). After optimization, the specific energy absorption (SEA) of the structure is significantly improved, while the initial peak stress (IPS) is decreased. The new structure proposed in this paper is expected to provide a novel design thinking and optimization idea for superstructure design. [ABSTRACT FROM AUTHOR]

Based on the traditional concave hexagonal honeycomb structure, three kinds of concave hexagonal honeycomb structures were compared. The relative densities of traditional concave hexagonal honeycomb structures and three other classes of concave hexagonal honeycomb structures were derived using the geometric structure. The impact critical velocity of the structures was derived by using the 1-D impact theory. The in-plane impact characteristics and deformation modes of three kinds of similar concave hexagonal honeycomb structures in the concave direction at low, medium, and high velocity were analyzed using the finite element software ABAQUS. The results showed that the honeycomb structure of the cells of the three types undergoes two stages: concave hexagons and parallel quadrilaterals, at low velocity. For this reason, there are two stress platforms in the process of strain. With the increase in the velocity, the joints and middle of some cells form a glue-linked structure due to inertia. No excessive parallelogram structure appears, resulting in the blurring or even disappearance of the second stress platform. Finally, effects of different structural parameters on the plateau stress and energy absorption of structures similar to concave hexagons were obtained during low impact. The results provide a powerful reference for the negative Poisson's ratio honeycomb structure under multi-directional impact. [ABSTRACT FROM AUTHOR]