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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 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]

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]

• 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]

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]

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]

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]

Auxetic metamaterials possess superior properties and have drawn extensive attention in the past decades. Herein, two curved ribs are added to the conventional re‐entrant (CRE) honeycomb structure to form a modified auxetic re‐entrant (MRE) honeycomb structure for improving the energy absorption capacity of the structure. In‐plane quasi‐static compression response of the honeycomb in large deformation is numerically explored first. Then, quasi‐static compression test is conducted to verify the validity of the numerical simulation. Both experimental and numerical simulation results reveal that during the quasi‐static compression process, two plateau stresses occur in the load–displacement curves of the structure, and the second plateau stress is much higher than the first one. The occurrence time of the second plateau stress can be controlled by the distance between the concave curved ribs in the structure. The experimental results are in good agreement with the finite element analysis results. Due to their desirable mechanical properties, the MRE honeycomb structures have great potential for applications in civil engineering, vehicle crashworthiness, and protective infrastructure. [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]

• 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]

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

Lightweight materials used for impact mitigation must be able to resist impact and absorb the maximum amount of energy from the impactor. Auxetic materials have the potential to achieve high resistance by drawing material into the impact zone and providing higher indentation and shear resistance. However, these materials must be artificially designed, and the large deformation dynamic effects of the created structures must be taken into consideration when deciding on a protection concept. Despite their promise, little attention has been given to understanding the working mechanisms of high-rate and finite deformation effects of architected auxetic lattice structures. This study compares the static and dynamic elastic properties of different auxetic structures with a honeycomb structure, a typical non-auxetic lattice, at equivalent mass and stiffness levels. In this study, we limit the investigation to elastic material behavior and do not consider contact between the beams of the lattices. It is demonstrated that the equivalent static and dynamic properties of individual lattices at an undeformed state are insufficient to explain the variations observed in impact situations. In particular, the initial Poisson's ratio does not determine the ability of a structure to resist impact. To gain a thorough comprehension of the overall behavior of these structures during localized, high rate compression, the evolution of the elastic tangent properties under compression and shear deformation was monitored, leading to a more profound understanding. Observations made in one configuration of stiffness and mass are replicated and analyzed in related configurations. [Display omitted] • Different lattice architectures are modeled using nonlinear Timoshenko beams. • Auxetic and non-auxetic lattices are compared for static and impact loading. • The lattice geometry is more decisive in impact mitigation than the Poisson's ratio. • Good impact protection is not guaranteed by a high initial Young's modulus. • Maintaining a high lateral pressure wave speed helps to distribute impact energy. [ABSTRACT FROM AUTHOR]

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]

Flexible piezoelectric sensors have received widespread attention in wearable electronics for their ability to convert mechanical energy into electrical energy, while the insufficient output power and complex preparation process have limited their application. In this work, several honeycomb structures based on graphene macro-film (GAMF) were created via laser engraving, which can utilize negative Poisson's ratio (NPR) properties to improve the output electric performance of flexible piezoelectric sensors. The effect of different electrode materials on the piezoelectric output was investigated in the experiments and compared with the theoretical equations, indicating that the output power of the sensor could be enhanced up to 142 % by improving the materials auxetic mechanical properties. The stability tests have proven that the sensors can operate effectively for a long time under different operating conditions. Moreover, the optimized sensor shows powerful potential for monitoring human movements such as finger tapping, joint bending, and foot stepping. This work opens up a new development path for the preparation of convenient and high-performance wearable electronic devices. The negative Poisson's ratio characteristic of the honeycomb graphene macro-film is used to increase the deformation of PVDF film to increase the electrical output performance of the flexible piezoelectric sensor. The optimized sensor can be used to detect human movements. [Display omitted] • Honeycomb graphene macro-films with different mechanical properties were prepared by laser engraving. • Flexible piezoelectric sensors based on honeycomb graphene macro-films are prepared. • The output performance of piezoelectric sensors can be improved by adjusting mechanical properties of electrode materials. • The flexible piezoelectric sensors can be used to detect human movements. [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]

An analytical model is formulated for 2-D periodic negative honeycomb thicken strut re-entrant lattice structures and a modified rounded corner negative honeycomb structure that shows negative Poisson's ratios (NPR). Analytical modeling is done using Castigliano's second theorem, where each beam is modeled using Timoshenko beam theory, considering bending, stretching, and transverse shearing. Elastic modulus and Poisson's ratio have been formulated for both structures in the form of non-dimensional geometrical characteristics, such as length ratios, angles of re-entrant arms, shear correction factor, and the material's Young's modulus and Poisson's ratios. Numerical simulations conducted in ABAQUS-CAE explicit solver validate the analytical model. The effect of the non-dimensional parameters on the qualities of the developed structure is demonstrated. It is observed that the structures with a low curvature ratio have a high fluctuation of Poisson's ratio and Elastic constant when plotted against the other parameters. The slenderness ratio has little impact on Poisson's ratio but significantly influences elastic modulus. It is shown that various needs can be satisfied by customizing the Poisson's ratios and elastic constant of both forms of lattice construction over an extensive range by carefully choosing the geometrical parameters and material. [ABSTRACT FROM AUTHOR]

• Effects of heating and cooling thermal shock on thermally induced vibration (TIV) are explored. • Influence of geometric nonlinearity under heating/cooling thermal shock forms is revealed. • The TIV characteristics of sandwich beams with auxetic honeycomb cores are discussed and compared with traditional honeycomb. • The instability conditions of the clamped beam with immovable ends under heating thermal shock are given. The nonlinear thermally induced vibration (TIV) characteristics of sandwich beams with auxetic honeycomb cores under general boundary conditions are studied. Based on first-order shear deformation theory, the dynamic governing equations are obtained through Hamilton principle, in which geometric nonlinearity and temperature dependence are considered. The temperature field along the thickness is calculated by finite element method and nonlinear TIV responses are solved via Newton-Raphson-Newmark method. The effects of temperature dependency, thermal shock forms, geometric nonlinearity, thicknesses of beam and face-sheet, boundaries and honeycomb geometrical parameters are studied. Results show that the reduction of the absolute inclined angle of the auxetic honeycomb can weaken the TIV responses. The influence of geometric nonlinearity on quasi-static and dynamic responses depends on the thermal shock form. Thermal buckling is the necessary condition for the occurrence of the TIV in clamped beams with immovable ends. Moreover, the research provides some design references to suppress the TIV responses of the sandwich beam with auxetic honeycomb core. [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]

In this paper, an analytical investigation is presented on the natural frequency analysis of sandwich plate resting on Winkler-Pasternak type elastic foundations in thermal environment. The sandwich plate consists of an auxetic honeycomb core with negative Poisson's ratio, which is assumed to perfectly bond to two carbon nanotube reinforced composite (CNTRC) face sheets to ignore potential interface effects or imperfections in bonding. The material properties of CNTRC are assumed to be temperature dependent. The volume fraction of carbon nanotube (CNT) varies through the thickness dimension according to linear functions with five different distribution patterns of CNT including UD, FG-O, FG-V, FG-Λ and FG-X. The governing equations of motion are derived based on the Reddy's first order shear deformation plate theory and Hamilton's principle, and the expression of the natural frequency is performed via Galerkin method. Artificial neural network (ANN) model is established to accurately predict the natural frequency of the sandwich plate on the basis of 1450 data points collected from analytical results. The effects of various material and geometrical parameters on the natural frequency of the sandwich plate are investigated in details. [ABSTRACT FROM AUTHOR]

Auxetic structures, which have a negative Poisson's ratio, have good mechanical energy/impact absorption properties. These structures have found application in sandwich composites in the aerospace and defence industries, in the production of armour or protective sports equipment. In this study, the mechanical behaviour of the auxetic honeycomb structure in different directions (in-plane and out-of-plane) under impact loading was investigated. For the in-plane (x and y) and out-of-plane (z) directions, boxes with an auxetic honeycomb structure were produced by material extrusion method using Power ABS filament. In the experimental study, dynamic tests were carried out with a drop test machine. Besides, explicit analyses were performed by creating finite element models for these 3 directions. The experimental and numerical results have shown that the energy absorption property of auxetic honeycomb geometry is superior in the case of out-of-plane loading, in agreement with each other. In in-plane loadings, crush force efficiency (CFE) and crush forces were lower. [ABSTRACT FROM AUTHOR]

3D printable multi-material honeycombs have attracted increasing interest recently due to the improved elastic moduli, buckling and energy absorption properties. This paper proposes an analytical homogenization for the equivalent in-plane elastic moduli (EIEM) of multi-material honeycombs. First, the axial and bending stiffness of a cantilever beam consist of three sections made of different materials is formulated. Then based on unit cell method and cantilever beam model, the closed-form expressions of EIEM are proposed by fully considering the deformations of both joints and cell walls with arbitrary stiffness, which are sufficiently general to be applied to hexagonal, auxetic and rectangular multi-material honeycombs and validated very well by numerical simulations and experiments. Furthermore, the effects of geometric and material distribution ratios on EIEM are discussed. The results show that the geometric and material distribution ratios of inclined cell wall have a significant effect on all five EIEM while that of vertical cell wall shows a significant effect on shear modulus but only a slight effect on y- direction elastic moduli. Compared with single-material honeycombs, changing joint stiffness has a significant effect on the equivalent Young's moduli and shear modulus but a slight effect on Poisson's ratios. • Closed-form expressions of equivalent elastic moduli for multi-material honeycombs. • Axial and bending stiffness formulated for a dual-material cantilever beam. • Analytical expressions of moduli match well with numerical and experimental results. • Dependency of material and geometric distributions on moduli investigated. • Proposed method applied to multi-material hexagonal and auxetic honeycombs. [ABSTRACT FROM AUTHOR]

Lantern, also known as coloured-lantern making, is known for being an ancient traditional craft in China that can be dated back as early as West Han Dynasty. Inspired by the lantern, the lattice element is built by vertically rotating and duplicating the 2D units, then the 3D auxetic metamaterial is formed by connecting the 8 ligaments of the lattice element on two perpendicular planes. As the elastic behaviors associated with this metamaterial are still almost unknown to a large extent, in this study, an analysis has been conducted to investigate how the geometric parameters related to the lattice design influence its elasticity. For this reason, a novel 3D lantern-shaped honeycomb structure (LSH) has been proposed, the Castigliano's second theorem, energy principle, and Moore's theorem are utilized to solve its Young's modulus and Poisson's ratio in the three main directions. The theoretical results exhibit good agreement with the numerical and experimental results. The results showed that the elasticity of LSH structures can be programmed by adjusting a range of geometric parameters. In addition, LSH features a bidirectional zero Poisson effect and a good stress distribution during compression. It shows potential in terms of load-bearing to meet the requirement of lightweight and high stiffness. This structure shows good promise for applications in aerospace, construction and other fields. [ABSTRACT FROM AUTHOR]

• The free vibration and nonlinear dynamic response of sandwich plates with an auxetic honeycomb core and piezoelectric face sheets are freshly addressed. • An analytical solution based on the first-order deformation plate theory and von Karman-type nonlinear strain-displacement relationship is established for movable simply supported and immovable simply supported plates. • The Galerkin and Runge–Kutta fourth-order methods are used to solve the system of nonlinear differential equations and capture the displacement-time and acceleration-displacement curves. • New parametric studies regarding the influence of the material, geometrical parameters, and elastic foundation coefficients, the geometrical parameters of the auxetic honeycomb core layer, as well as the electric boundary condition on the free vibration and nonlinear dynamic response of piezoelectric-auxetic sandwich plates are examined. This article analyses the nonlinear dynamic behavior and the free vibration of a piezoelectric auxetic honeycomb sandwich plate resting on a Pasternak elastic substrate. The plate includes two face sheets of piezoelectric material and an auxetic honeycomb core with a negative Poisson ratio. The first-order shear deformation plate theory, together with the von Kármán type nonlinear strain-displacement relationship, is used to establish the nonlinear equations of motion. Linear electric potential change with piezoelectric layer thickness is assumed. Two types of boundary conditions, namely immovable and movable simply supported, are considered. The displacement-time and acceleration-displacement curves under dynamic loads are determined by using the Galerkin and Runge-Kutta fourth-order methods. Verification examples have been performed and confirmed the accuracy of the model. Finally, several novel investigations have been conducted to evaluate the effect of material, geometrical parameters, and elastic substrate coefficients on the frequency and nonlinear dynamic characteristics of piezoelectric auxetic honeycomb sandwich plates for both open-circuit and closed-circuit operation. [ABSTRACT FROM AUTHOR]

Mechanical metamaterials represent a class of deformable systems, which exhibit macroscopic deformations, mechanical, and/or thermal properties. These emerge due to the structure of their subunits rather than their materials composition and typically exhibit anomalous (normally negative) macroscopic structural, mechanical, or thermal property/properties caused by a change in shape/size of the system. Herein, a class of honeycombs is discussed, which push to the extreme the classical definition of "mechanical metamaterials," exhibiting temperature‐tunable Poisson's ratio properties. More specifically, centrosymmetric honeycombs with T‐shaped joints constructed from different materials are shown to exhibit temperature‐dependent Poisson's ratio values, which can be either positive or negative (auxetic) depending on the external stimulus the system is subjected to. The sign and magnitudes of the Poisson's ratio values are explained in terms of particular geometries that these composite honeycomb systems attain at different temperature conditions. In particular, auxeticity is attributed to the transformation of the T‐shaped units to re‐entrant units. Practical aspects on how these properties may be achieved are discussed, including the possibility that the changes in shape, and hence Poisson's ratios, are induced via different extents of dryness on opposite surfaces of ligaments made from absorbent materials. [ABSTRACT FROM AUTHOR]

Honeycombs or foams with reentrant microstructures exhibit effective negative Poisson's ratio. Although they are light weight due to inherently empty space, their overall stiffness and damping are somewhat limited. With judiciously chosen filler material to fill the voids in star‐shaped honeycomb, it is numerically demonstrated its auxeticity may be enhanced. By combining the filler and skeleton, the hierarchical composite materials are constructed. The magnitude of the enhancement depends on inner and outer filler's modulus mismatch, as well as the types of filling. Filler's auxeticity also largely enhances overall auxeticity of the outer‐ and all‐filled honeycomb. In addition, for outer‐filled honeycomb, its effective viscoelastic modulus and damping are significantly increased, while maintaining relatively light weight, due to local stress concentration. [ABSTRACT FROM AUTHOR]

The nonlinear mechanical responses of tetrachiral honeycombs under large deformation are theoretically analyzed by employing elliptic integrals, and the results are verified by numerical simulations. The nonlinear relationships between normal stress, shear stress, Poisson's ratio and the strain are derived for the tetrachiral honeycombs. It is found that the Poison's ratio of the tetrachiral honeycombs under large deformation is totally different from that under small deformation. The Poisson's ratio can achieve to a large magnitude of 0.8 in the former case, while remains 0 in the latter case. Moreover, the tetrachiral honeycombs exhibit positive Poison's ratio under large tensile-deformation, whilst showing negative Poisson's ratio under large compression-deformation. The magnitude of Poisson's ratio depends on both the honeycomb's deformation and the ligament relative length, while it is insensitive to the ligament thickness. Besides, the coupling effect between tensile (or compression) and shear is observed for the tetrachiral honeycombs. In other words, shear deformation appears within the honeycomb under uniaxial loading. The coupling effect depends on both the honeycomb's deformation and the geometric parameters of the cell structure. And the quantitative relationships among them are derived. This special coupling effect of tetrachiral honeycombs provides a new idea for designing more metamaterials. [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]

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]

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]

Auxetic mechanical metamaterials that exhibit a negative Poisson's ratio (NPR) can be artificially designed to exhibit a unique range of physical and mechanical properties. Novel sandwich structures composed of uniform and gradient auxetic double arrowhead honeycomb (DAH) cores were investigated in terms of their vibration and sound transmission performance stimulated by nonhomogeneous metamaterials with nonperiodic cell geometries. The spectral element method (SEM) was employed to accurately evaluate the natural frequencies and dynamic responses with a limited number of elements at high frequencies. The results indicated that the vibrating mode shapes and deformations of the DAH sandwich models were strongly affected by the patterned gradient metamaterials. In addition, the sound insulation performance of the considered DAH sandwich models was investigated regarding the sound transmission loss (STL) from 1 Hz to 1500 Hz under a normal incident planar wave, and this performance was compared with that for hexagonal honeycomb sandwich panels. A programmable structural-acoustic optimization was implemented to maximize the STL while maintaining a constant weight and high strength. The results showed that the uniform DAH sandwich models with larger NPRs generally exhibited better vibration and acoustic attenuation behaviors and that the optimized gradient increasing NPR models yielded higher STL values than the optimized gradient decreasing NPR models for two specified frequency cases, with improvements of 6.52 dB and 2.52 dB and a higher bending stiffness but a lower overall STL. Thus, sandwich panels consisting of auxetic DAHs can achieve desirable vibroacoustic performance with a higher bending stiffness than conventional hexagonal honeycomb sandwich structures, and the design of gradient DAHs can be extended to obtain optimized vibration and noise-control capabilities. [ABSTRACT FROM AUTHOR]

A 3D re-entrant honeycomb structure was designed in a simple configuration by introducing a spatial angular design parameter. Mechanical responses under uniaxial compression of it at constant spatial angle (α) and different re-entrant angles (θ) were investigated both experimentally and theoretically. Designed lattice auxetic structures with high shape fidelity were fabricated using selective laser sintering (SLS) of PA 2200 powder. The produced samples exhibited negative, zero, and positive Poisson's ratios depending on a selected θ value, and their mechanical properties varied over a wide range. Bend- and buckling-dominated deformation mechanisms of the struts have been observed under compression. Additionally, the analytical models of re-entrant honeycomb structures effectively illustrated the quantitative relationships between their mechanical properties (Young's modulus (E) and Poisson's ratio) and the design parameter θ. The results presented in this study would provide a reference to the customized design of the porous auxetic structures with unique mechanical properties. [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]

Based on Love shell theory and equivalent single layer theory, a new method is proposed in this paper to analyze the dynamic response of honeycomb sandwich pipe under the action of moving pressure. The results of displacement response under two boundary conditions are within 3.5% error range with the FEM results. The theoretical model takes into account the effect of thickness, and the calculation results are more accurate compared with the FSDT method, which can be used for both thin-walled and thick-walled pipes. By analyzing the effects of honeycomb structure parameters and pipe dimensions on the critical velocity and displacement response of honeycomb sandwich pipe, theoretical guidance is provided for the design of new pipeline structures. • A novel mathematical procedure has been presented to study the vibrational behaviour of a composite cylindrical shell consisting of elastic-isotropic skin and a zero Poisson's ratio cellular core under moving pressure. • The equations of motion have been extracted based on the classical shell theory and Hamilton's principle. • A detailed parametric study was carried out to investigate the sensitivity of the geometric parameters and material properties of the honeycomb core to the natural frequency, critical velocity and displacement response of the sandwiched cylindrical shell. • The research of this paper provides theoretical guidance for the structural design of new honeycomb pipeline. [ABSTRACT FROM AUTHOR]

Nonlinear dynamic behavior of double curved shallow shells with negative Poisson’s ratios in auxetic honeycombs on elastic foundations subjected blast, mechanical and damping loads is investigated in the present article. This study considers double curved shallow shells with auxetic core which have three layers in which the top and the bottom outer skins are isotropic aluminum materials; the central layer has honeycomb structure using the same aluminum material. Based on the analytical solution, Reddy’s third order shear deformation theory (TSDT) with the geometrical nonlinear in von Karman and Airy stress functions method, Galerkin method and the fourth-order Runge-Kutta method, the resulting equations are solved to obtain expressions for nonlinear motion equations. The effects of geometrical parameters, material properties, elastic foundations, imperfections, blast loads, mechanical and damping loads on the nonlinear dynamic analysis of double curved shallow shells with negative Poisson’s ratios in auxetic honeycombs are studied. [ABSTRACT FROM AUTHOR]

This paper presents a finite-element analysis of honeycomb and re-entrant honeycomb structures made of a two-phase composite material which is optimized with respect to selected parameters. It is shown that some distributions of each phase in the composite material result in the counter-intuitive mechanical behaviour of the structures. In particular, negative values of effective Poisson's ratio, i.e., effective auxeticity, can be obtained for a hexagonal honeycomb, whereas re-entrant geometry can be characterized by positive values. Topology optimization by means of the method of moving asymptotes (MMA) and solid isotropic material with penalization (SIMP) was used to determine the material's distributions. [ABSTRACT FROM AUTHOR]

• The non-Fourier thermal fracture of an auxetic honeycomb layer investigated theoretically. • The temperature field will be unaffected by non-Fourier effects if t / τ * > 12.2. • The non-Fourier effect reduces the thermal shock resistance by 34%. • The auxetic property can enhance the thermal shock resistance. Auxetic honeycomb layer (HL) is a typical metamaterial with a negative Poisson's ratio. In this paper, the thermal shock fracture problem of the auxetic HL is investigated based on non-Fourier heat conduction. The uncracked non-Fourier temperature and thermal stress field are determined by the separation of variables method and the constitutive model of auxetic HL. The corresponding thermal stress intensity factor (TSIF) is obtained in numerical form. Based on the TSIF and the fracture toughness criterion, the critical temperature of auxetic HL is predicted. There is a clear difference between the results based on the non-Fourier and Fourier models. The maximum thermal stress and TSIF of the auxetic HL obtained from the non-Fourier model are both significantly higher than those obtained from the Fourier model. If non-Fourier effects are not taken into account, the critical temperature of the auxetic HL is also overestimated. In addition, the auxetic property can increase the critical temperature of the HL, whether based on the non-Fourier or Fourier model. The results demonstrate the good potential of the auxetic HL in the thermal protection system application. [ABSTRACT FROM AUTHOR]

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

• Optimizing the inclined beams in re-entrant structural elements into buckling beams. • Improved structural element and negative Poisson's ratio metamaterial are designed. • The problem of stress concentration in structural elements is alleviated. • The negative Poisson's ratio characteristic of metamaterial is enhanced. Aiming at the problems of stress concentration and negative Poisson's ratio in the deformation process of the re-entrant structure, a cosine-shaped re-entrant structure negative Poisson's ratio metamaterial is proposed in this paper. By optimizing the inclined beams in the re-entrant structural elements into single cosine, tandem cosine and multiple cosine buckling beams, different configurations of improved re-entrant structural elements are designed. Finite element modeling and quasi-static compression simulations and experiments are carried out for single and periodically arranged re-entrant structures. The results show that the comprehensive stress of the single cosine structure and the tandem cosine structure are reduced by 18.7% and 58%, respectively, and the maximum stress can be reduced by 6.7% and 5.2%, respectively. In addition, the negative Poisson's ratio of metamaterial with a single cosine re-entrant structure is increased by 14% compared with that before the improvement. [ABSTRACT FROM AUTHOR]

In the present work, a new design of honeycomb is proposed by embedding the rhombic configuration into the normal re-entrant hexagonal honeycomb (NRHH), in order to enhance the honeycomb’s in-plane mechanical properties. Both theoretical analysis and numerical simulations are employed to calculate the in-plane mechanical properties of the new honeycomb under uniaxial compression, including Young’s modulus, Poisson’s ratio and critical buckling strength. The results show that the new honeycomb can maintain auxetic performance, while both the in-plane Young’s modulus and the critical buckling strength are significantly improved compared to the NRHH. Comparisons between the present design and other exiting enhanced periodic topologies are also carried out. With respect to them, the present design features superior performances. For these outstanding properties, this layout may provide a new concept for the optimization and design of auxetic materials. [ABSTRACT FROM AUTHOR]

A preliminary study of the mechanical properties of auxetic cellular material consisting of re-entrant hexagonal honeycombs is presented. For different scales of the honeycombs, the finite element method (FEM) and experimental models are used to perform a parametric analysis on the effects of the Poisson's ratio (cell angle) and the relative density (cell thickness) of honeycombs on bearing capacity and dynamic performance of the auxetic material. The analysis demonstrates that the ultimate bearing capacity of the presented auxetic cellular material is scale-independent when the Poisson's ratio and the relative density are kept constant. The relationship between the geometric parameters and vibration level difference of the honeycombs is also revealed, which can be divided into two converse parts around the Poisson's ratio v = -1.5. When v is smaller than -1.5, increasing the cell thickness leads to an increase in the vibration level difference of the honeycombs. Moreover, the dynamic performance of thin-walled honeycombs is greatly influenced by the scale of the honeycombs, especially for the ones with small Poisson's ratio. These conclusions are verified by a frequency response test and a good agreement between the numerical results and experimental data is achieved. [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]

[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]

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]

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]

• 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]

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]

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]