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The main objective of this paper is to evaluate the dynamic behaviour of sandwich toroidal shells composed of a core with negative Poisson ratio (auxetic honeycomb material) and nanocomposite enriched coating layers under impulsive/periodic pressures considering the geometrical nonlinearity. The set of nonlinear equilibrium equations based on the first-order shear deformation theory are and the resultant nonlinear differential motion equations are approximately solved by the Galerkin method and 4th-order Runge–Kutta solution, respectively. The achieved responses show that the amplitude of outward deformations is intensively increased when the proposed sandwich shells are subjected to rectangular periodic and impulsive loadings which shows the destructive effects of this type dynamic loading. The performed parametric studies shows that these destructive effects can be controlled by changing the geometrical properties of the honeycomb cells and the volume fractions of the nanocomposites in the coating layers. It is notable that in the previous studies the nonlinear dynamic response of toroidal shells subjected to various periodic and impulsive pressures was not investigated. However, in the present work, the mentioned dynamic responses were achieved and investigated without spending time-consuming computational. In fact, the novelty of this work is to develop such a robust and efficient tool. [ABSTRACT FROM AUTHOR]

• 3D origami-inspired auxetic honeycomb with omni-directional high stiffness is proposed. • Theoretical models for predicting the elastic mechanical properties of the CFRP composite 3D honeycombs are developed. • The 3D honeycomb can be applied where good load-bearing capacity and obvious auxetic effect are simultaneously desired. • The 3D honeycomb suggests a potential for 3D isotropic auxetic design. Traditional 3D auxetic materials face significant limitations, marked by low stiffness and pronounced anisotropy. To address these challenges, here a new kind of 3D origami-inspired auxetic honeycomb with omni-directional high stiffness is proposed by us. Two simplified theoretical models based on different assumptions are developed to predict structural homogenized elastic properties along the principal axes. Combined theoretical and numerical studies are carried out to reveal the auxetic mechanism and dominated deformation characteristics of the 3D honeycomb. In order to gain a understanding of its elastic anisotropy, directional dependence of structural homogenized Young's moduli, Poisson's ratios and shear moduli are also investigated in detail. A detailed examination of the dependence of structural homogenized Young's moduli, Poisson's ratios, and shear moduli on loading direction is conducted to comprehend its elastic anisotropy. This paper introduces a feasible method for the rapid manufacturing of the 3D honeycomb using high-performance continuous carbon fiber reinforced composite (CFRP) based on hot-pressing molding. Subsequently, the compressive elastic behaviors of CFRP 3D honeycombs are characterized and evaluated through experimental tests. A comparison with traditional 3D auxetic materials reveals the 3D honeycomb's superiority in both multi-axial loading and rapid manufacturing. Additionally, the demonstrative example suggests that the 3D honeycomb can offer nearly isotropic Poisson's ratio of about −0.9. These results not only demonstrate that the 3D honeycomb is an excellent candidate for applications where both good load-bearing capacity and notable auxetic effect are simultaneously desired but also highlight its potential for 3D isotropic auxetic design. [ABSTRACT FROM AUTHOR]

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

• A class of modified hexagonal honeycomb to realize pattern transformation. • Honeycomb's elastic constants are derived by theoretical energy analysis. • Honeycomb structures exhibit auxetic behavior after pattern transformation. • The cell/node of the honeycomb has a rotating behavior after pattern transformation. • The underlying mechanism of pattern transformation is revealed for honeycomb. Pattern transformation, as one of the special properties of mechanical metamaterials, is widely found in elastic porous structures and gradually expanding to honeycomb structures. Inspired by the higher-order flower-like buckling pattern of hexagonal honeycomb, and generalizing the geometry of structures that pattern transformation occurs under uniaxial compression, this paper proposes a Modified Hexagonal Honeycomb(MHH) structure by adjusting the thickness ratio α and the deflection extension angle θ of the cell wall to topologically reconstruct the honeycomb structure to initiate the first-order quasi-flower-like buckling pattern under uniaxial loading. Results show that the quasi-flower-like pattern transformation appears directly for the MHH structure under uniaxial compression, accompanied with a transition of the Poisson's ratio, from positive to negative. And the butterfly pattern, which appears for traditional hexagonal honeycomb only under biaxial loading, is also observed for the MHH under uniaxial compression. The relative size of the nodes among cell walls is believed to play a crucial role on the appearance of the pattern transformation of the honeycomb structure. This work has revealed the underlying physical mechanism for pattern transformation of honeycomb structures, and would also extend the application range of honeycomb structures to the design of elastic dampers, bending/torsion actuators, or robot drive joints. [ABSTRACT FROM AUTHOR]

Recently, auxetic metamaterials have turned into an area of growing interest, because of their deformation uniqueness, design flexibility, and functional diversity. To achieve their programmable design of densification and energy absorption, the variable stiffness factor method (VSF) emerged. However, the energy absorption capacity of the metamaterials designed by this method has a significant reduction. In this work, to remedy this defect, several different lightweight specimens are proposed and fabricated to extend the stage of energy absorption and retain the tunability. Then quasi-static compression tests and finite element methods are carried out to analyze the mechanical properties of the designed boundary-constrained structure (BCS) and X-shape constrained structure (XCS). The accuracy of the densification points and energy absorption capacity of the two structures at different VSF values are also studied. The results show that the densification points of the designed structures can be adjusted quantitatively, and their deformation modes are more stable than conventional structures during compression. Furthermore, their specific energy absorption is four and five times higher than that of non-lightweight structures with VSF = 40%, respectively. These findings contribute to advancing the implementation of auxetics in applications of multistage protective structures. • A lightweight metamaterial based on the variable stiffness factor (VSF) method is proposed. • The proposed structures realize multi-level energy absorption and stable deformation. • The SEA of proposed structures was 4 and 5 times higher than that of VSF = 40% structure. [ABSTRACT FROM AUTHOR]

Re-entrant anti-trichiral honeycomb is a typical auxetic material. The collapse process can be divided into three stages while its negative Poisson's ratio (NPR) effect under large deformation is still unclear. In the present paper, the NPR effects of re-entrant anti-trichiral honeycombs under large deformation are studied by numerical and theoretical method. Numerical results are verified by the experiments with respect to their deformation mechanism and stress-strain behavior. Theoretical formulas are derived to predict the NPR effect of the honeycomb under large deformation. The analytical predictions are in good agreement with the FEM results. It is revealed that the NPR effect of the honeycomb is magnified with the global strain in the second stage while is weaken in the third stage of the deformation process. The decrease of the ligament-ratio and the mean radius will result in more obvious NPR effect. Variation of cell-wall thickness doesn't have much impact on the Poisson's ratio in the second stage, while smaller cell-wall thickness will induce larger NPR in the third stage. The present work is supposed to shed light on the design and fabrication of re-entrant anti-trichiral honeycombs with desired Poisson's ratio. Image 1 • Analytical predictions of the NPR effect under large deformation exhibits a good agreement with the numerical results. • A special deformation mechanism and stress-strain behavior are illustrated by the experiments and numerical simulations. • The negative Poisson's ratio (NPR) of the honeycombs varies differently with strain at different stages. • Variation of cell-geometry parameters greatly influence the NPR effect of the honeycombs. • More evident NPR effect is exhibited when the honeycomb gradually develops into the conventional re-entrant honeycomb. [ABSTRACT FROM AUTHOR]

• In-plane crushing responses of the tetra-chiral (TC) honeycombs were investigated by using experimental and numerical methods. • Theoretical formulas were derived to predict plateau stresses of the TC honeycomb under both quasi-static and dynamic crushes. • Effects of unit cell radius ratio on crushing strength, dynamic sensitivity index and effective Poisson's ratio (EPR) of the TC honeycomb were investigated. • Stress and EPR evolutions of the TC honeycomb with different orthogonal array ratios were also investigated. Tetra-chiral (TC) honeycombs are a type of auxetic materials showing negative Poisson's ratio (NPR), which are promising for impact energy absorption. This study aims to analyze the in-plane crushing response of the TC honeycombs under both quasi-static and dynamic loading conditions through numerical simulations and theoretical analyses. The numerical modeling techniques in LS-DYNA were validated using the quasi-static crush test data of TC honeycomb specimens obtained with a 3D-printer. Numerical simulations revealed the "Z" mode deformation and the "bulge effect" under quasi-static crushing, and the row-by-row "I" mode deformation under dynamic crushing of the TC honeycombs. By referring to the simulation results, theoretical models were derived based on the representative unit for predicting the TC honeycomb's crushing strength, i.e. plateau stress, under both quasi-static and dynamic loads. Good agreement was found between the theoretical and the numerical predictions with a maximum relative error of 7%. Parametric analyses showed that the unit cell configuration has a great effect on the crushing strength of TC honeycomb under in-plane crushing. The dynamic sensitivity index was defined to quantitatively evaluate the sensitivity of the TC honeycomb's crushing strength to the loading speed, and was found to depend on the unit cell geometry. The TC honeycomb was found to present a varied effective Poisson's ratio (EPR) with strain under both quasi-static and dynamic in-plane crushing; smaller radius ratio and lower crushing speed were found to yield more obvious NPR effect. Moreover, relative dimension of the TC honeycomb represented by the orthogonal array ratio do not affect its plateau stress under either quasi-static or dynamic crushing, while large orthogonal array ratio results in more obvious "bulge" and NPR effects under quasi-static crushing. Image, graphical abstract [ABSTRACT FROM AUTHOR]

Highlights • Fracture behavior of auxetic cellular structures is investigated. • A ductile damage computational modeling technique is presented. • Identification of ductile damage material parameters is given. • The influence is evaluated of the shape of unit cells on fracture behavior. • Experimental testing is carried out to validate the numerical results. Abstract Auxetic cellular structures are advanced materials with negative Poisson's ratios, which exhibit some unique features which are useful for various applications. The objective of this paper is the numerical simulation and experimental analysis of evolution propagation under quasi-static loading conditions in selected auxetic cellular structures with different geometries and orientations of unit cells that is: (i) honeycomb structure, (ii) re-entrant structure, and (iii) rotated re-entrant structure. The failure modeling capability of Simulia Abaqus code for ductile materials is used for the numerical simulation. The paper presents in detail the calculation methodology for determination of ductile damage material parameters that, are used for further numerical simulations of the damage initiation and evolution. Standard Compact Tension (CT) specimens are selected for the numerical simulation and experimental testing. Here, the specimens are made from 7075-T651 aluminum plate, cut using water jet cutting technology. Using a numerical approach, the fracture behavior of the selected auxetic structures is estimated first. Experimental testing is also carried out to validate the numerical results. The comparison between computational and experimental results regarding crack propagation path and force-displacement diagrams showed a reasonable agreement. [ABSTRACT FROM AUTHOR]

Abstract It is generally acknowledged that the indentation resistance or hardness of auxetic materials is higher than that of their conventional counterparts under elastic deformation. However, this property of the auxetic material may not always be superior to that of the non-auxetic materials when the deformation is relatively large with plasticity considered. In this study, we come up with an index to quantitatively depict the indentation resistance of the hexagonal honeycombs under large deformation. The indentation resistance of both the auxetic and non-auxetic hexagonal honeycombs is compared and discussed. Results show that in the premise of honeycombs possessing the same relative density, the indentation resistance of auxetic hexagonal honeycombs is not always higher than that of the non-auxetic honeycombs. This phenomenon is verified by the numerical simulations. Further analysis shows that there is a critical value of the absolute value of Poisson's ratio, which is determined by the cell-wall length ratio, to estimate the higher indentation resistance between the auxetic and non-auxetic hexagonal honeycombs. The influence of indentation velocity is also analyzed based on numerical simulations. This present work is supposed to shed light on the design and evaluation of the indentation resistance for both auxetic and conventional honeycombs. [ABSTRACT FROM AUTHOR]

In order to comprehensively understand the dynamic response of auxetic honeycombs, theoretical analysis are conducted to predict the NPR effect and the crushing stress of the re-entrant hexagonal honeycomb. The honeycomb’s crushing stress is a function of the cell’s geometric parameters, crushing velocity and the mechanical property of the cell-wall material. Results show that the crushing stress enhances with the increasing crushing velocity. A dynamic sensitivity index is employed to quantitatively evaluate this enhancement. It is shown that small cell-wall angle, low relative density or high cell-wall length ratio of the honeycomb attribute high velocity-sensitivity to the crushing stress. The Poisson’s ratio of the re-entrant honeycomb is also expressed as a function of the cell’s geometric parameters. It is revealed that the NPR effect enhances with the increasing cell-wall angle and the decreasing cell-wall length ratio. All the theoretical predictions are verified by numerical simulations. Besides, an interesting phenomenon is noticed that the crushing velocity has significant influence on the honeycomb’s NPR effect at the early stage of crushing. However, this influence almost vanishes when the overall strain is larger than about 0.2. This present work is supposed to shed light on the design of the auxetic honeycomb. [ABSTRACT FROM AUTHOR]

• Two different assembled honeycomb structures were designed and studied. • The structures can be transformed by changing the length of connection plates. • The energy absorption capacity of re-entrant honeycomb was investigated. • Re-entrant honeycomb has higher energy absorption than hexagonal honeycomb. Fabricating auxetic metamaterials via an assembling process is a novel and economic method. In this work, an assembled structure that could realize the conversion of positive and negative Poisson's ratio by changing the length of the connection plates was proposed. Two different honeycomb structures of the assembled re-entrant honeycomb (ARH) and assembled hexagonal honeycomb (AHH) were designed, manufactured and studied numerically and experimentally. Dimensions of the two assembled honeycomb structures are consistent. The nominal stress–strain curves of the two assembled honeycombs have similar initial peak stresses, but the assembled re-entrant honeycomb has a higher bearing capacity and shorter stress plateau. Subsequently, the mechanical properties of ARH were studied by changing the three parameters of corrugated plates. Besides, the energy absorption and specific energy absorption of the assembled re-entrant honeycomb were investigated through the numerical method. Finally, the assembled honeycomb structure with the suitable parameter was determined. Tunable mechanical properties of the assembled auxetic structures can be obtained by varying the length of the connection plates. This strategy of assembly can reduce the costs of manufacturing and improve transportation efficiency. The proposed assembled structures are promising in civil and protective engineering. [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 novel re-entrant auxetic honeycomb metamaterial with zigzag inclined ligaments is proposed. • The proposed metamaterial can be conveniently fabricated by low-cost traditional manufacturing。 • Theoretical formulae for the effective elastic constants of the proposed metamaterial are developed. • The proposed metamaterial possesses tailorable mechanical properties. Conventional two-dimensional (2D) re-entrant auxetic honeycomb is one of the earliest examples of auxetic metamaterials. Recently, plenty of 2D re-entrant honeycomb variants are developed to enhance their stiffness. However, the stiffness enhancement for most of the existing designs is generally obtained with compromising the conjugated auxeticity. Moreover, most of the existing designs are hard to be fabricated by low-cost traditional manufacturing technology due to their complex architectures. The present work aims to enhance the stiffness without compromising the conjugated auxeticity, and yet retains its convenience and low-cost for fabrication. By introducing zigzag inclined ligaments, a novel 2D re-entrant auxetic honeycomb metamaterial is firstly proposed. Based on Castigliano's second theorem, a theoretical model of the proposed design is established to facilitate the understanding of the underlying microstructural mechanisms. The obtained analytical solutions, as validated by systematic finite element (FE) analyses, elucidate different roles of the microstructural geometry on the effective mechanical properties of the proposed re-entrant auxetic honeycomb metamaterial. Compared with the conventional re-entrant auxetic honeycomb, which is a particular case of the present design, both the stiffness and the auxeticity along specific principal directions of the present design are improved remarkably. [ABSTRACT FROM AUTHOR]

An analytical framework has been developed for predicting the equivalent in-plane elastic moduli (longitudinal and transverse Young’s modulus, shear modulus, Poisson’s ratios) of irregular auxetic honeycombs with spatially random variations in cell angles. Employing a bottom up multi-scale based approach, computationally efficient closed-form expressions have been derived in this article. This study also includes development of a highly generalized finite element code capable of accepting number of cells in two perpendicular directions, random structural geometry and material properties of irregular auxetic honeycomb and thereby obtaining five in-plane elastic moduli of the structure. The elastic moduli obtained for different degree of randomness following the analytical formulae have been compared with the results of direct finite element simulations and they are found to be in good agreement corroborating the validity and accuracy of the proposed approach. The transverse Young’s modulus, shear modulus and Poisson’s ratio for loading in transverse direction (effecting the auxetic property) have been found to be highly influenced by the structural irregularity in auxetic honeycombs. [ABSTRACT FROM AUTHOR]

Sandwich panels/sacrificial cladding systems composed of an auxetic core sandwiched between two faceplates can be considered an effective protective measure for reinforced concrete structures from blast loads. In this study, the effectiveness of re-entrant honeycomb core sandwich (RHS) protective panel systems, which exhibit a negative Poisson's ratio, to protect one-way simply supported reinforced concrete (RC) slabs subjected to a close-range detonation from high explosive charges was experimentally evaluated. Three large-scale field blast trials were carried out, namely an RC slab without protection as the reference test and two RC slabs with RHS protective systems under similar blast loading conditions. The RC slabs with RHS protective systems experienced catastrophic failure, unlike the unprotected reference slab that experienced only localised concrete damage. LS-DYNA numerical models were validated and agreed well with the experimental results. It was demonstrated that the transferred blast impulse to the main structure can be magnified by a factor of 1.6 by using an RHS protective system compared to an unprotected structure. Furthermore, the effect of the mass of the protective system was numerically studied. The numerical results showed that the blast protection level of the main structure is governed by the inertial resistance of the protective system rather than through energy absorption of the auxetic honeycomb core structure. • Response of RC panels protected by auxetic sandwich panels to close-in explosion is investigated experimentally and numerically. • The damage magnification effect of the auxetic sandwich panels is captured experimentally which has not been reported so far. • The impulse transferred to the main structure could be magnified by a factor of 1.6 compared to the unprotected structure. • The duality of energy absorption and inertial resistance of auxetic protective systems need to be considered at close standoff distances. [ABSTRACT FROM AUTHOR]

The nonlinear dynamic behaviour of sandwich shell panels having auxetic honeycomb core and facesheets composed of composite material with curvilinear fibres is investigated for the first time. A finite element study is performed considering a third-order shear deformation theory incorporating Murakami zig-zag effects for the analysis of the variable stiffness composite laminate (VSCL) auxetic honeycomb sandwich panels. A nine-noded C0 isoparametric quadratic shell element with eleven degrees of freedom per node is considered and von Kármán nonlinear strain-displacement equations are used to include the geometrical nonlinearity. The linear free vibration and nonlinear transient response of the panels are obtained using the eigenvalue solution and Newmark's time integration scheme, respectively. Most of the auxetic sandwich structures considered in the literature are made up of aluminium metal and therefore, the authors explored the viability of the VSCL based auxetic sandwich panels. A thorough numerical study including the effects of the geometrical parameters of the honeycomb unit cell, curvilinear fibre path angles and boundary conditions on the nonlinear dynamic response of auxetic sandwich panel with negative Poisson's ratio is presented. • Analysed linear free vibration and nonlinear transient response of the VSCL based auxetic sandwich shells panels. • A finite element formulation based on Murakami zig-zag theory with eleven degrees of freedom per node is developed. • A novel auxetic sandwich panel having VSCL facesheets and honeycomb core with negative Poisson's ratio is investigated. • The curvilinear fibre orientation of the VSCL facesheets influences the vibrational response of the auxetic shell panels. [ABSTRACT FROM AUTHOR]

[Display omitted] • An assembled auxetic chiral honeycomb (AACH) is designed and manufactured by 3D printing. • The AACH could exhibit lower peak force and high stress plateau. • The external energy is mainly absorbed by the vertical wave plate. • The AACH provides a new idea for the industrial manufacturing of auxetics. Auxetic metamaterials tend to be fabricated using additive manufacturing and laser cutting due to their special porous microstructures. Although the auxetic metamaterials have many applications currently, the high cost and the low efficiency of available manufacturing are adverse to expend their application range. In this work, the auxetic chiral honeycomb is assembled crosswise using the slotted wave plate. Effects of wave radius, plate thickness, slot percentage, and base material on the Poisson's ratio and mechanical performance are explored experimentally and numerically. The results show that assembled auxetic chiral honeycomb (AACH) exhibits lower peak force and high plateau stress than the conventional assembled one. With the increase of wave radius and plate thickness, the energy absorption (EA) and specific energy absorption (SEA) would increase. As for the different material combinations, when the base materials in vertical and horizontal wave plates adopt stainless steel and aluminum, respectively, the AACH would exhibit desirable EA, SEA, and auxetic behavior. These findings provide a new approach to the manufacture of auxetics at a low cost, which is beneficial for potential applications. [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]

Double arrowed honeycomb (DAH) is a typical auxetic material with negative Poisson's ratio (NPR) and excellent mechanical properties, showing a wide application prospect in aerospace, marine, automotive and other fields. In this work, we introduce the double circular arc walls into the regular DAH unit cell to improve the strength and energy absorption capability of the material. According to the position of the arc wall, three circular double arrowed honeycomb (CDAH) unit configurations were proposed, including upper-circular (U-type), lower-circular (L-type), and full-circular (F-type). The prototype specimens of DAH and CDAHs were fabricated by 3D printing and tested under quasi-static crushing. The finite element (FE) models of the specimens were established and validated by the experimental results. The experimental and numerical results showed that the three types of CDAHs have higher crushing stress, crush force efficiency (CFE) and specific energy absorption (SEA) than the DAH with the same geometric parameters, which is due to the formation of more plastic hinges at the joints and the middle of the arc walls. Specifically, the CFE of L-type CDAH is 25.8% higher than that of DAH, and the SEA of F-type CDAH is 85.9% higher than that of DAH. The detailed parameter analyses of CDAH revealed that small short inclined wall angle and lower circular arc radius, and large friction coefficient value, long inclined wall angle and cell wall thickness all lead to large SEA. Among the three types of CDAH, the U-type has the greatest SEA and the most NPR effect under the same relative density. Finally, a wide range of SEA and Poisson's ratio of the CDAH can be obtained by rationally designing the arc wall position and the geometric parameters of the unit cell. [Display omitted] • Quasi-static crushing behaviors of three novel types of circular double arrowed honeycombs (CDAHs) through experimental tests and numerical simulations. • More Energy absorption than regular double arrowed honeycomb (DAH) due to formation of more plastic hinges of arc walls. • Good agreement between experimental and numerical results in terms of deformation mode, crushing stress and specific energy absorption (SEA). • Effects of cell number, geometric parameter and relative density on crushing responses of CDAHs. [ABSTRACT FROM AUTHOR]

In this paper, a new design of auxetic honeycomb is proposed for mechanical performance enhancement by combining the arc-shaped wall and the normal double-arrowed auxetic configuration. On basis of Mohr's 2nd theorem and Castigliano 2nd theorem, an analytical model considering strut bending and stretching is developed to modulate the in-plane mechanical properties of the proposed honeycomb with the geometric parameters. Further, an integrated experimental, simulation and theoretical approach is carried out to investigate its elastic properties and Poisson's ratios in a wide range. The comparison shows that the theoretical results are in good agreement with the experimental and simulation results, verifying the established analytical model. The results reveal that both the in-plane modulus and the Poisson's ratio of the proposed auxetic honeycomb are simultaneously improved compared to the typical double-arrowed and the re-entrant hexagonal designs, and show high and diverse dependencies on the geometric parameters. Additionally, the honeycomb features a stiffer modulus and stronger auxeticity along y direction than that along x direction when the arc angle of "bone", θ 1 , not exceeding a "turning point". The present design may provide an extensive reference for the design and application of mechanical meta-materials. [ABSTRACT FROM AUTHOR]

Due to the negative Poisson's ratio (NPR) effect, auxetic structures such as re-entrant honeycombs show excellent energy absorption and force mitigation capabilities under crushing load. Compared with two-dimensional (2D) auxetic structure, three-dimensional (3D) ones are expected to have better performance, but they are more difficult to fabricate. In this study, a hierarchical fabrication method for metallic 3D re-entrant honeycomb (3D-RH) using traditional manufacturing techniques is proposed. A 3D-RH specimen was crafted and tested under quasi-static crushing condition. The finite element (FE) model was established and verified by the experimental results. The numerical simulation results showed that the friction condition between 3D-RH specimen and loading surfaces has a great influence on the deformation mode of specimen. Moreover, the energy absorption capability of 3D-RH was numerically compared with a similar structure, i.e., the warp and woof periodic auxetic cellular (WWPAC) structure. The results showed that the specific energy absorption (SEA) of 3D-RH is 1.59 times that of WWPAC and the 3D-RH outperformed the latter in lightweight performance. Finally, the blast resistance of 3D-RH sandwich panel was numerically studied. Compared with 2D re-entrant expanded honeycomb (2D-REH) core, 3D-RH core can reduce the maximum deflection of lower face-sheet by 14.6%, and increase SEA by 20.5%, showing better blast resistance. • A hierarchical fabrication method of metallic 3D-RH has been proposed. • The method uses traditional manufacturing techniques to reduce fabrication cost. • The friction coefficient can alter the deformation mode of 3D-RH under crushing. • The energy absorption per unit mass of 3D-RH is greater than that of the WWPAC. • The 3D-RH shows better anti-blast performance than the 2D-REH. [ABSTRACT FROM AUTHOR]

In this work, an analytical model of a 3D re-entrant honeycomb auxetic cellular structure has been established based on both a large deflection beam model and a Timoshenko beam model. Analytical solutions for the modulus, Poisson’s ratios and yield strength of the cellular structure in all principal directions were obtained, which indicate a wide range of mechanical property control via geometrical designs. The results were compared with experimentation and finite element analysis, and it was verified that the analytical model provides a convenient and relatively accurate method in the prediction of the performance for the auxetic cellular structures once the manufacturing related factors are adequately incorporated into the model. It was also found that the model provides less accurate predictions when higher-order coupling effects such as warp locking becomes significant under lower structural symmetry. [ABSTRACT FROM AUTHOR]

Double arrowhead honeycombs (DAHs) are auxetic cellular materials with negative Poisson's ratio (NPR). The quasi-static and impact behaviors of both uniform and functionally graded DAHs are explored. Analytical expressions for the in-plane Young's modulus, Poisson's ratio and quasi-static yield stress of uniform DAHs are derived and are found to be consistent with finite element (FE) predictions, showing that the quasi-static yield stress of DAHs is dependent upon the geometrical parameters and NPR. Systematical simulations of uniform DAHs subject to different impact velocities reveal that there exists a critical impact velocity beyond which the dynamic plateau stress is insensitive to the effect of NPR. A semi-empirical expression of the plateau stress is obtained. For functionally graded DAHs, they are shown to only have improved energy absorption capacity under high velocity impacts. Moreover, the results of uniform DAHs are shown to be able to be adopted to interpret the simulated plateau stress of functionally graded DAHs under impact loading. The deformation mechanisms associated with the impact resistance of DAHs are also discussed. [ABSTRACT FROM AUTHOR]

Abstract: Systems with a negative Poisson’s ratio (auxetic) exhibit the unusual yet very useful property of getting wider rather than thinner when uniaxially stretched. A novel mechanism to generate auxetic behaviour at tailor-made values which may be implemented in composites manufacture using readily available materials is proposed. FEA simulations are used to provide a proof of principle for this concept and an analytical model is proposed so as to elucidate the requirements for auxetic behaviour. It is shown that the simulations and analytical model give comparable results and confirm that this system may reach giant negative values of the Poisson’s ratio. [Copyright &y& Elsevier]

• A novel composite is proposed by filling layered re-entrant honeycombs with concrete. • The mechanical properties and failure modes of two types of specimens under uniaxial compression are investigated. • The proposed auxetic composite exhibits an enhanced stiffness and shear resistance. • The effects of cell angle and cell wall thickness on the mechanical properties are investigated. Auxetic materials exhibit desirable mechanical properties, e.g., fracture resistance, shear resistance and energy dissipation due to their unique deformation characteristics. Honeycomb sandwich structures also have superior properties, e.g., energy absorption performance and low density. These desirable characteristics enable them as promising alternatives for building construction to meet the modern construction requirement which a higher safety standard is needed. In this study, a novel concrete composite with auxetic layered honeycomb was designed, manufactured and investigated for exploring the load-bearing performance of auxetic metamaterials under quasi-static compression. The layered honeycomb sandwich structure was analyzed by quasi-static compression test and its energy absorption performance was evaluated. Numerical models, validated by experimental results, were employed in parametric studies to further examine their performance. The results show that the layered structure has higher initial peak stress and stable platform stress. Moreover, it could improve the shear resistance and overall stability of the structure. These findings are beneficial to the applications of auxetic metamaterials in building construction. [ABSTRACT FROM AUTHOR]

A novel class of two-dimensional auxetic structures based on the pentagon motif is proposed. Their mechanical properties are investigated by combining molecular mechanics simulations with a simple three-parameter mechanical model which assumes perfectly elastic behavior. It is predicted that the proposed structures – termed as double re-entrant honeycomb – may possess unique mechanical characteristics, which include complete and perfect auxeticity, as well as the negative Poisson's ratio observed in both the tensile and compressive regimes. The behavior of the considered structures is explained in relation to well-known auxetic models. It is shown that the considered structures simultaneously implement three different mechanisms leading to a negative Poisson's ratio: the opening of the re-entrant units, the rotation of the squares, and the flattening effect. [Display omitted] • A novel class of 2D auxetic structures composed of pentagons is proposed. • The proposed structures combine two overlapping re-entrant honeycomb structures. • Simultaneous implementation of three different auxetic mechanisms is possible. • The proposed structures offer unique properties: complete and perfect auxeticity. [ABSTRACT FROM AUTHOR]

Cellular auxetic materials possess a negative Poisson's ratio (NPR) and attractive mechanical properties; however, these materials are limited by their low stiffness and strength and strong anisotropy. To address these issues, we developed a novel auxetic honeycomb with a fully triangular architecture inspired by the anti-tetra chiral configuration. The new stretch-dominant structure was fabricated using a three-dimensional printing process. The resulting deformation behavior of the triangular auxetic honeycomb structure was compared with that predicted from finite element (FE) simulations; these revealed an NPR and high stiffness, in which the ratio of specific stiffness to specific density was 0.12. The simulations allowed for an NPR in both the longitudinal and transverse directions concurrently. Based on the mechanism revealed by the FE simulations, the novel triangular honeycomb can be tuned to have the same behavior in two orthogonal directions, while retaining high stiffness and an NPR. [ABSTRACT FROM AUTHOR]

This work investigates the effects of cracking on the overall properties of brittle auxetic/non-auxetic honeycombs. The micro numerical model and macro theoretical model are established simultaneously. The analytical expressions of crack opening displacement (COD) are derived and the results agree well with numerical simulations. The fracture toughness of honeycombs is calculated by combining the stress in the numerical model and the stress intensity factor (SIF) in the theoretical model. The reductions in the equivalent stiffness and equivalent thermal stress coefficient (TSC) of the cracked honeycombs are predicted. The negative Poisson's ratio (NPR) effects on those fracture mechanics parameters and equivalent thermomechanical properties are studied. And considering the orthogonal anisotropic properties of honeycombs, the cracking along two orthogonal directions is examined. It reveals that the significant NPR effects can only be detected in a single direction and the effects in another direction are inconspicuous. In addition, the effects of crack length, medium dimensions, and cell-wall angle of honeycomb cells on the overall performance of the cracked medium are also evaluated by parametric studies and the results are displayed graphically. [ABSTRACT FROM AUTHOR]

In this study, a new vertical strut combined re-entrant auxetic structure was designed and its mechanical behaviors have been studied. An analytical model was established based on energy theorems considering bending, shearing and stretching. Numerical simulations and experiments were both carried out to confirm the validity of the analytical model based on beam theory. Results exhibited a good agreement between the refined analytical model, the numerical simulation and experimental study. Four deformation mechanisms were analyzed and the effect of deformation on the effective Poisson's ratio (EPR) and elastic module were investigated. A parametric study was further performed to quantitatively illustrate the influences of the geometrical parameters on the effective elasticity properties of the designed structure. The results showed that the lightweight structures can significantly enhance the auxetic behavior and achieve a high degree of anisotropy with wide vertical strut lengths and internal angles compared with conventional re-entrant honeycomb configurations. • An analytical model of a vertical strut combined auxetic structure was established. • Vertical strut and re-entrant angle mainly determined effective elasticity properties. • Four deformation mechanisms were considered and influenced auxetic behaviors. • Numerical simulations and experiments both validate the analytical model. [ABSTRACT FROM AUTHOR]

In this article, a novel re-entrant octagonal honeycomb (ROH) with negative Poisson's ratio (NPR) configuration is proposed owing to its superior energy absorption and lightweight design performances. Regarding the effects of adjacent unit cells, a mechanics-based homogenization approach is put forward and employed to derive static mechanical properties including elastic modulus and Poisson's ratio of two-dimensional (2D) and three-dimensional (3D) ROHs under axial loading. Based on above, the predominant compression failure mode is explored. Then, the static mechanical properties and finite element model of ROH are validated by experiment and demonstrate high accuracy. Subsequently, to obtain dynamic responses of the ROH under dynamic impact loading, the relations among dynamic plateau stress and quasi-static plateau stress, initial density, dense strain and impact velocities are established under the conditions of mass conservation and momentum theorem based on one-dimensional shock wave theory and ideal rigid-perfectly plastic material model. Besides, dynamic energy absorption models of the ROH under dynamic loading are acquired in consideration of the effects of impact velocities on dense strain, the results show that theoretical models agree quite well with simulation results. On this basis, the application of ROH on automotive energy absorber is studied with the purpose of acquiring superior energy absorption and satisfying lightweight requirements simultaneously. Based on the decoupling thought of stiffness and pedestrian protection, a new design method of carbon fiber reinforced plastics (CFRP) hood with ROH is put forward in consideration of energy absorption and lightweight requirements. Of this, ROH is regarded as sandwich structure to meet the demands of energy absorption, CFRP plates are treated as outer and inner skins to satisfy the needs of stiffness. Firstly, multi-objective optimization models are set up under the constraints of reasonable structural parameters and negative Poisson's ratio. Then, the NSGA-Ⅱalgorithm is adopted to achieve the optimal Pareto fronts with the targets for maximum unit mass energy absorption and minimum density. Afterwards, the optimization on thicknesses of CFRP layers is carried out to achieve minimum mass under the constraint conditions that the static stiffness of CFRP hood is larger than that of steel hood. In addition, the layering sequence of inner and lower skins are also optimized. Finally, improved overall stiffness, optimized HIC values and similar lightweight space of CFRP hood with ROH are achieved in comparisons with CFRP hood without ROH. Compared with steel hood, the pedestrian protection performance of CFRP hood with ROH is greatly enhanced, 1st free mode increases by 33.9%, and torsional stiffness and bending stiffness increase by 23.1% and 30.8%, respectively. While the weight decreases by 40.1%. The results indicate that the CFRP hood with ROH presents outstanding advantages of pedestrian protection and lightweight design in terms of HIC and stiffness performance. [ABSTRACT FROM AUTHOR]

Nowadays, sandwich plates with cellular core structures are gaining the attention of researchers owing to their outstanding features. For a better insight into auxetic structures, in this study, we propose an excellent computational approach based on polygonal meshes to comprehensively examine the free vibration, buckling and dynamic instability behaviors of the auxetic honeycomb sandwich plate structures. A generalized C 0 -type higher-order shear deformation theory ( C 0 -HSDT) in conjunction with both Laplace and quadratic serendipity shape functions is employed to approximate the strain fields for polygonal plate elements. The sandwich plate structures are constituted by an auxetic honeycomb core layer with negative Poisson's ratio and two skin layers reinforced by graphene nanoplatelets (GNPs). Ultra-light features of the plate structures can be obtained by using the auxetic honeycomb cells with negative Poisson's ratio while the GNPs are embedded into skin layers to enhance the structural stiffness. In order to determine the dynamic instability region of the sandwich plate, Bolotin's approach is utilized in the current research. Several numerical examples are carried out to investigate the influences of geometrical parameters of auxetic cell and GNPs reinforcement on the structural behaviors. The results obtained in the current research can be considered as benchmark ones to investigate auxetic sandwich plate structures. [ABSTRACT FROM AUTHOR]

This paper presents a stiffening method by which new inclined walls are added to the classical re-entrant honeycomb cell. This modification boosts the in-plane rigidity of the re-entrant cell without significant loss from auxetic behaviour. This study focuses on the in-plane elasticity moduli and negative Poisson's ratios along the principal axes. Analytical expressions that calculate the elasticity moduli and negative Poisson's ratios are derived; both finite element modelling and experiments reported in the literature validate the expressions of this work. Further, the variation in the in-plane elastic properties of the core cell is examined by altering the new wall's geometric, sectional, and material parameters. The results from the analytical expressions and the finite element models match very closely and demonstrate the boosted rigidity of the cell proposed in this work. This work also provides a benchmark of the new cell against the classical cell that can be used to tailor the in-plane elasticity moduli and negative Poisson's ratios to suit the needs of different applications. • Enhancement stiffness of re-entrant honeycomb core cell. • Advanced tunable mechanical properties by new derived analytical expressions. • A benchmark of analytical, numerical and experimental results. [ABSTRACT FROM AUTHOR]

• The experimental and numerical methods were used to investigate the dynamic response of end-clamped shallow sandwich arch with HCNPR under local impulsive. • The local negative Poisson's ratio deformation was observed in the reentrant honeycomb core. • The dynamic deformation evolution of the face sheets and honeycomb core was studied. In recent years, auxetic metallic cellular material such as auxetic reentrant honeycomb is one of the research hotspot in metallic cellular materials due to its attractively negative Poisson's ratio. In this manuscript, the dynamic response of the end-clamped shallow sandwich arch with aluminum face sheets and auxetic reentrant hexagonal aluminum honeycomb core subjected to foam projectile with high-velocity impact was experimentally and numerically investigated. The reentrant honeycomb cores with different cell-wall thicknesses were fabricated by selective laser melting (SLM). The deformation processes of honeycomb core were captured by a high-speed camera. And deflection history of back face sheet was obtained using three-dimensional digital imaging correlation method (DIC) analysis system. Failure modes and deformation mechanisms of the sandwich arch were investigated. According to experiment results, the local negative Poisson's ratio deformation was found in honeycomb core. Then, a finite element (FE) model was established to study the dynamic deformation evolution of two face sheets and auxetic reentrant honeycomb core. The results showed that the honeycomb cells were not always undergoing shrinkage deformation and flowing into the loading center, while the local expand deformations of honeycomb core were also found. [ABSTRACT FROM AUTHOR]

In recent years, auxetic cellular materials such as auxetic reentrant honeycombs were widely studied due to its attractively negative Poisson's ratio. In this manuscript, the structure response of end-clamped sandwich beam with auxetic reentrant hexagonal aluminum honeycomb core locally subjected to foam projectile with high-velocity impact was experimentally and numerically studied. The reentrant honeycomb cores with different cell-wall thicknesses were fabricated by selective laser melting (SLM). According to experiment results, the failure modes of the sandwich beam were investigated. It was found that sandwich beam with different honeycomb cell's thicknesses could fail in different modes. Meanwhile, the local negative Poisson's ratio deformation was observed in the thin honeycomb core. Based on this, a finite element (FE) model was constructed to analysis the dynamic deformation evolution of two face sheets and auxetic reentrant honeycomb core. The local auxetic and expand deformations of honeycomb core were both found. Finally, the residual deflections of sandwich beam under impulsive loadings were discussed. Unlabelled Image • The structure response of sandwich beam with reentrant honeycomb core under locally impact was firstly studied. • The local negative Poisson's ratio deformation was observed in the reentrant honeycomb core. • The relationship between residual deflection of sandwich beam with reentrant honeycomb core and local impulse was linear. [ABSTRACT FROM AUTHOR]