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

The influence of unit cell geometric parameters on the thermal fracture behavior and thermal shock resistance of honeycomb ceramics sandwich structures is revealed for the first time. The present study establishes a continuum model for the thermal fracture of sandwich structures, and a discrete numerical representation model for the equivalent fracture toughness of honeycombs, respectively. A novel evaluation approach for the thermal shock resistance of porous material structures has been provided by combining the two models. The effects of temperature dependence, face sheet thickness, honeycomb orientation and honeycomb geometrical parameters on thermal shock resistance are studied. Results indicate that changing the inclined angle of honeycomb can effectively increase the critical thermal shock temperature rise. Auxetic honeycomb sandwich structures with the inclined angle of −9° can reach the peak of the critical temperature rise. The results would contribute to the application of honeycomb sandwich structures in thermal protection systems. • Thermal shock resistance of honeycomb sandwich structures was evaluated through continuum model and numerical model. • The influence of honeycomb geometric parameters on equivalent fracture toughness was revealed. • The critical temperature rise of sandwich structures with honeycomb cores of different unit cells was predicted. • The inclined angle is the key parameter to improve the thermal shock resistance of honeycomb sandwich structures. [ABSTRACT FROM AUTHOR]

• Hybrid re-entrant/hexagonal CF/PA12 honeycombs were 3D printed via FFF. • Temperature-dependent mechanical and piezoresistive characteristics were evaluated. • Hybrid honeycombs excel in enhancing in-plane strength (+64 %) and energy absorption (+125 %). • Hybrid honeycombs exhibit remarkable strain-sensing abilities, boasting gauge factors of ∼146. • The hybrid honeycombs retain 40–60 % of their mechanical properties at 125 °C. This study investigates a novel self-sensing honeycomb composite structure composed of two distinct cellular layers with differing unit cell architectures, specifically hexagonal and re-entrant designs. Short carbon fiber (CF)/polyamide 12 (PA12) composite filaments with 0, 5 or 15 wt.% CF content were utilized to additively manufacture the honeycomb structures via Fused Filament Fabrication (FFF), and their mechanical and piezoresistive self-sensing characteristics were experimentally investigated under quasi-static in-plane and out-of-plane compression at both room temperature and elevated temperatures. The results reveal that the hybrid hexagonal/re-entrant (HR) honeycombs mechanically outperform their non-hybrid double-layer and single-layer counterparts under in-plane loading, reporting an increase in collapse strength and energy absorption by factors of 1.64 and 2.25, respectively. These improvements are attributed to the mechanical interactions occurring at the interface between the auxetic and non-auxetic layers within the hybrid structure, effectively enhancing its structural attributes. Furthermore, the double-layer honeycombs display excellent strain-sensing capabilities within the elastic regime, with gauge factors reaching values as high as 146. Mechanical tests conducted at elevated temperatures reveal that the CF/PA12 honeycombs retain a significant portion of their elastic modulus, strength and energy absorption even at 125 °C, while maintaining high gauge factors of up to 72.4. These honeycombs also exhibit pronounced thermoresistive behavior, evidenced by a decrease in electrical resistance of up to 41.3 % with increasing temperatures from 25 to 125 °C. Considering their exceptional combination of thermo-mechanical, thermoresistive and piezoresistive characteristics, these hybrid double-layered CF/PA12 honeycombs hold promise for potential applications in multifunctional lightweight structures, offering integrated temperature and strain-sensing capabilities. [Display omitted] [ABSTRACT FROM AUTHOR]

• A novel bi-material multistable auxetic honeycomb (BMAH) with reusable and enhanced energy-absorbing phases was designed. • The crushing stress–strain curve shows three stress plateaus, and BMAH maintains a stable Poisson's ratio even at high strain levels, transitioning from near-zero to negative and then to positive. • Under the selected material combination, the second stress plateau is 8 times greater than the first, and the third stress plateau is 17 times greater than the first, significantly improving energy absorption efficiency. • A theoretical model was established to reveal the deformation mechanism of BMAH and predict the plateau stresses and strain range for each deformation stage. • Effects of geometrical parameters and crushing velocity on BMAH stress plateaus and Poisson's ratio were investigated, and a programmable guide for designing stress plateaus and specific energy absorption is presented. The ideal energy absorption structures, in addition to possessing reusability and high energy absorption efficiency, should also possess multiple desired properties to fulfill various functional applications. In this study, a bi-material multistable auxetic honeycomb (BMAH) is fabricated by using bi-material 3D printing technology. Under in-plane crushing, multiple stress plateaus can be achieved and the Poisson's ratio can be stably tuned, allowing for a transition from near-zero to negative and then to positive. The above characteristics are attributed to the specimen's multi-path deformation. The first stress plateau is only associated with recoverable elastic deformation. The second and third stress plateaus, which are 8 times and 17 times higher respectively than the first, are associated with plastic deformation, significantly enhancing energy absorption efficiency. The deformation mechanism is theoretically analyzed, and the effects of geometric parameters on the performance of BMAH are investigated. In addition, the effect of crushing velocity on the crushing behavior of the BMAH is also discussed. As the crushing velocity increases, the total number of stress plateaus transitions from three initially to two and then to one. The developed BMAH exhibits significant potential applications in multi-stage energy absorbers and smart sensors. [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]

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]

This paper examines the impact of polyurethane foam (PUF) filling on the dynamic response of honeycomb sandwich beams (HSBs) through the blast testing. The HSBs are composed of steel face sheets and an aluminium alloy honeycomb core filled with PUF. A comparative analysis of damage modes is conducted between conventional hexagonal and auxetic HSBs, considering both foam-filled and unfilled configurations. The results reveal that the HSBs with foam filling demonstrate significantly enhanced blast performance compared to their counterparts without foam filling. This superiority is evident in both global deformation and local damage characteristics. Furthermore, a well-validated numerical model is developed to examine the damage mechanisms of PUF-filled HSBs under blast loading. The investigation reveals that appropriate PUF filling methods can effectively enhance bending resistance while minimizing the decline in the energy absorption efficiency. Finally, a multiobjective optimization was conducted using the back-propagation (BP) neural network and the SPEA2 algorithm to identify the optimal position for PUF. By utilizing a reduced foam filling approach as opposed to completely filling the structure, the two optimized configurations show a decrease in deformation of 5.38 % with an equivalent specific energy absorption (SEA) or an increase in the SEA by 5.26 % with an equivalent deformation. [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]

• 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]

Light composite materials such as auxetic honeycomb structures offer a unique combination of strength, lightweight, and durability, making them ideal for a wide range of industrial and structural applications. Consequently, it is crucial to study the effect of these materials on the dynamic behavior of structures. In this study, an analytical solution based on the multiple-scale method has been proposed to solve equations of motion of a multilayer axisymmetric annular plate. The plate includes two top and bottom isotropic layers and one auxetic honeycomb core layer. By considering both radial and transverse deflections, the governing equations are derived based on the first-order shear deformation theory. The radial and transverse frequencies of the plate are determined from the order zero of equations and a correction coefficient for each frequency has been extracted from the order one and solvability conditions. The response of the plate under harmonic transverse excitation has been determined analytically and by conducting a parametric study, the effect of different geometrical and mechanical parameters on the free and forced vibration responses has been studied. It is observed that employing a honeycomb core in the multilayer plate allows us to significantly decrease the plate weight while the dynamic response and the frequencies remain nearly the same or vary slightly. The results are validated by comparing them with the finite element method and some other references. • An analytical solution for the free and forced vibration of an auxetic composite annular plate is proposed based on the FSDT. • By employing the multiple-scale method, a correction factor for the natural frequencies is determined. • The effect of different combinations of boundary conditions on frequencies is investigated. • The forced vibration lateral and axial responses to a harmonic excitation are determined. • The effect of the auxetic honeycomb layer on the vibration behavior of the plate is studied. [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]

• 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]

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]

Auxetic lattice structures are known for their superior stiffness-to-density and strength-to-density ratios. Re-entrant hourglass exhibits an acceptable equivalent elastic modulus and remarkable energy absorption capacity among various auxetic configurations due to their flexibility and hinge deflecting during crushing loads. This study introduces a curved hourglass honeycomb which can be produced using 3D printing with pure or reinforced filaments incorporating continuous fibers. New closed-form formulations are analytically derived using an energy method by considering an extracted unit cell to predict the equivalent in-plane mechanical properties for the first time. The plateau stress of the proposed honeycomb is evaluated at the densification state of a unit cell using the energy conservation theory, equating external work with plastic energy dissipation. The accuracy of these extended relations is validated against experimental outcomes, demonstrating good agreement between analytical and experimental results. Additionally, robust linear and nonlinear finite element analyses are conducted to assess the accuracy of the obtained relations, including the equivalent stiffness and plateau stress for structures produced with reinforced filaments. The nonlinear finite element code employs appropriate subroutines to model plasticity/damage events. Based on the established analytical relations for stiffness and plateau stress, multi-objective optimization using Genetic Algorithm is applied to define optimum values for the Pareto front chart's objective functions of stiffness and plateau stress. The optimization process involves exploring the design space and defining the values of geometrical parameters to achieve the desired objectives. In conclusion, this study presents a novel approach to developing curved re-entrant honeycomb structures, with analytical formulations validated against experimental and numerical results. Optimization helps to identify optimal configurations concerning stiffness and plateau stress, offering potential applications in lightweight and high-strength materials design. According to the obtained results, for selection of the best value for curved strut angle which results in the optimum value of stiffness and plateau stress, a range between 10°-34° can be considered depending on the volume fraction of fibers. [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]

Modern engineering extensively employs complexly curved shell structures, presenting mathematical challenges in analyzing their mechanical behavior due to geometric intricacies. The recent trend of incorporating advanced lightweight materials into these structures drives the need to develop improved theories and methods. This study presents an investigation into the free vibration analysis of barrel-shaped sandwich (BSS) shells using a modified thick shell theory (MTST). These sandwich shells feature functionally graded (FG) ceramic-metal layers on both inner and outer surfaces, with a lightweight honeycomb core. Notably, the honeycomb layer's thickness surpasses that of the inner and outer layers, necessitating the application of thick shell theory for accurate analysis. However, previous studies have often used classical theories for thin shells, and those applying thick shell theory sometimes neglected the curvature effects in the fundamental equations and rotary inertia components. Thus, this research employs the MTST to overcome these limitations. The study includes comparative validations and explores the impact of material parameters and curvature radii on the natural frequencies of these barrel-shaped sandwich shells through numerical examples. [ABSTRACT FROM AUTHOR]

This study is the first of its kind to apply an analytical technique to offer an accurate solution for the static buckling and static bending of functionally graded (FG) sandwich nanobeams, in which the core layer is an auxetic honeycomb. One notable aspect of this work is the use of third-order shear deformation theory for the computations. It is worth noting that the displacement field of the nanobeam is contingent upon a single parameter. This approach enables the resolution of stability and static bending issues encountered in nanobeams including auxetic honeycomb cores, while also providing a realistic depiction of the beam's mechanical behavior. The two surface layers are composed of different materials, each of which has mechanical characteristics that change in accordance with the exponential function law. The precise solution described in this work is very adaptable and may be used to investigate the mechanical behavior of beams with different boundary constraints, taking into consideration the effect of the nonlocal parameter. When the angle α of the cell varies, the honeycomb core's mechanical characteristics, such as Poisson's coefficient and elastic modulus E , vary continually. This results in static bending and buckling responses that are distinct from those of other auxetics. This study also found it intriguing that the wall angle α has a value of around 90° and that sandwich nanobeams have the highest load capacity. In addition, numerical calculations have been performed to demonstrate the influence of certain geometrical parameters, materials, and boundary constraints on the critical buckling load and maximum deflection of the nanobeam. • This study is the first of its kind to apply an analytical technique for the static buckling and static bending of FG sandwich nanobeams, in which the core layer is an auxetic honeycomb. • This study offers calculation findings demonstrating the effect of geometrical factors, materials, and boundary conditions on the ultimate load response and maximum displacement of FG sandwich nanobeams. • It is discovered that a certain value for the wall angles of the core layer cell yields the highest possible performance from this beam. [ABSTRACT FROM AUTHOR]

In this study, a model for the nonlinear dynamic analysis of the geometrically imperfect sandwich beam with functionally graded material (FGM) facets and auxetic honeycomb core is proposed. The auxetic feature of the honeycomb material is realized by a homogenization method, which gives the expressions of the effective material coefficients in terms of material property and cellular geometric parameters. The nonlinear motion equation of the geometrically imperfect beam is derived based on the Reddy's higher shear deformation theory, von Kármán nonlinear theory, as well as general geometric imperfection function. The thermal effect on the material properties and structural rigidity is also taken into account in this model. The Newmark method and Newton–Raphson iterative method are employed to solve the nonlinear motion equation of the sandwich beam. In numerical examples, the dynamic response of the sandwich beam under two types of load, i.e. moving load and impulse load, are discussed in details. The influences of various factors (such as material parameter, geometric imperfection, and thermal condition) on the nonlinear dynamic behaviors of the sandwich beam are elaborately investigated. The numerical results show those factors can play significant roles in the bearing ability, structural stiffness, or nonlinear dynamic behaviors of the sandwich beam in certain conditions. Some key conclusions on the influences are drawn from the numerical results, which can be a useful reference for future investigations. [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]

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]

• 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]

• A novel auxetic honeycomb (NAH) combined with chiral and re-entrant was proposed. • The EA and SEA of NAH are improved under Quasi-static compression and impact. • Under high-velocity impact, the EA of NAH is better than hexagonal honeycomb. • NAH with thickness gradient shows obvious auxetic behavior under high-velocity impact. Auxetic metamaterials as a cutting-edge field have attracted extensive attention from researchers because of their peculiar deformation mode and excellent mechanical properties. However, the unstable deformation and low stiffness of auxetic structure limit their potential development. To address these limitations, a novel auxetic honeycomb (NAH) has been proposed by combining an original re-entrant hexagonal honeycomb (RH) with cross-chiral honeycomb (CH). The proposed structure has higher stiffness than RH, and more stability than CH. Additionally, the stiffness, densification point, and auxetic behavior can be adjusted by the angle of cell ribs (θ). In this study, the static mechanical properties and deformation behavior of NAH are investigated experimentally and numerically. Furthermore, the energy absorption and deformation behavior of NAH under different impact loadings (low-, medium- and high-velocity) are investigated numerically. Finally, a series of functionally graded NAHs with varying thicknesses are studied to improve the impact resistance of NAH. The results show that NAH has better specific energy absorption than RH and CH under static compression. Moreover, NAH with θ < 90 ° exhibits greater energy absorption capacity compared to NAH with " θ > 90°" at high-velocity impacts. [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]

Auxetic structures have theoretically superior bending resistance that was previously inaccessible. Compared with the planar two-dimensional (2D) auxetic structures, the three-dimensional (3D) counterparts may exhibit auxetic behavior in multiple directions. Recently, increasing studies have been devoted to studying the mechanical properties of 3D auxetic structures. In this paper, two 3D honeycomb structures were proposed, namely 3D re-entrant honeycomb and 3D hexagonal honeycomb. Subsequently, the mechanical properties, deformation modes, and deformation mechanisms of these two honeycomb structures under three-point bending were investigated experimentally and numerically. Compared with the 3D non-auxetic hexagonal honeycomb, the 3D auxetic re-entrant honeycomb exhibits higher ductility and fracture resistance. In addition, unlike the conventional honeycomb structure, the mid-span section of the 3D auxetic honeycomb exhibits a trapezoidal deformation mode under bending. Finally, the influence of the number of unit cells and geometric parameters on the mechanical properties of the 3D honeycomb structure were systematically studied by parametric analysis. The excellent bending performance provides a basis for the application of auxetic honeycomb in the fields of biomedicine, soft robots, and buffer devices. [Display omitted] • Two 3D honeycomb structures, namely 3D auxetic honeycomb and 3D non-auxetic honeycomb, were designed and fabricated. • The mechanical properties, failure modes, and deformation mechanism of two specimens are investigated under three-point bending. • Compared with the 3D non-auxetic honeycomb, the 3D auxetic honeycomb exhibits better ductility and a trapezoidal deformation pattern at midspan. [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]

[Display omitted] • Spinal interbody cages adapted for an auxetic, and honeycomb using standard CAD software operations and manufactured with SLM. • Auxetic-based cages exhibit higher strength properties than honeycomb-based cages. • The stiffness of the auxetic cages is comparable to stiffness of human cortical bone. • The honeycomb cages exhibit lower value of Young's modulus closer to that for vertebrae. This paper presents a method for modeling a biomedical device by adaptation a commercially available interbody cage for an auxetic metamaterial and honeycomb structure using standard operations in Computer-Aided design software. The mechanical properties of experimental prototypes of Ti-6Al-4 V cages made by selective laser melting using computer modeling (finite element analysis), static and low-cycle fatigue compression tests (up to 3500 cycles) are characterized. 3D printed cells with structures with an angle of inclination between cell edges of less than 90˚ (auxetic metamaterial) are shown to exhibit higher static compressive strength and fatigue resistance than cells based on structures with an angle of inclination greater than 90˚ (honeycomb structure). The changes in the inclination angle differently affect to the porosity and consequently to mechanical behavior of auxetic metamaterial and honeycomb structure. The Young modulus of the auxetic-based interbody cage is 6.68 ± 0.28 GPa and comparable to the elastic modulus of human cortical bone. The honeycomb-based cage exhibits lower values of Young modulus (1.19 ± 0.03 GPa) close to that of trabecular bone and vertebrae. Importantly, the auxetic-based cage is not destroyed after 3500 cycles under 14 kN load with residual deformations ≤ 1 % (0.21 ± 0.10 mm displacements). [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]

• 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]

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

• 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]

• Blast experiments were conducted to study the close-in blast effect and failure characteristics of honeycomb HSPs. • The blast performance of auxetic HSPs is compared with regular hexagonal HSPs. • Simulation is in good agreement with experiments and can describe the deformation and fracture damage. • The effect of the core type and unit-cell angle on the damage of HSPs is investigated. 3D-printed auxetic honeycomb sandwich panels (HSPs) have considerable potential for blast resistance enhancement. This study aims to bridge the gap with regard to the experimental data on the effect of 3D-printed auxetic hexagonal honeycomb cores on the blast response of HSPs. To this end, the blast resistance of HSPs developed using auxetic re-entrant and regular hexagonal honeycomb cores is investigated experimentally and numerically. First, six HSPs are tested under close-in blast loadings. The HSPs comprise Q345 steel top and bottom sheets as well as a honeycomb aluminum alloy core with two configurations (regular hexagonal and auxetic re-entrant). According to the results, the former configuration enhances the HSP blast resistance by not only decreasing the deformation of the HSPs but also improving their damage tolerance. In addition, the responses of the HSPs are numerically studied via finite element analysis. The numerical method using the finite element program LS-DYNA achieves reasonable accuracy. Finally, a parametric study is conducted to investigate the effects of the honeycomb type, cell angle, debonding effects, and core material on the blast resistance of the HSPs. The results demonstrate that employing auxetic hexagonal honeycomb core, smaller cell angle, and ductile core material can improve the blast resistance of HSPs. [ABSTRACT FROM AUTHOR]

The literature on energy harvesting using piezoelectric materials is firmly concentrated on structures like cantilever beams with piezoelectric layers. In the present research, a piezo harvester made of a honeycomb sandwich panel is studied. The modeled sandwich panel is made of an auxetic core and two carbon nanotube-reinforced face sheets. It will be shown that this harvester offers more flexibility in its stiffness, leading to better performance in harvested energy. The displacement field of the panel is formulated in a general form, which includes different types of shear deformable plate theories. Within these plate models, transverse shear stresses and rotary inertias are taken into account. A piezoelectric layer is integrated at the top of the honeycomb substructure, and vibrations are originated from an external harmonic source. The material properties of the carbon nanotubes vary lineally in the thickness direction. Hamilton's principle is adopted to derive governing equations of motion, and then weighted residual method is applied to discretize the coupled differential electro-mechanical equations of motions. After validating the model, a detailed parametric study is carried out to investigate the impacts of different parameters such as auxetic cell characteristics, carbon nanotube volume fraction, carbon nanotube configuration, and geometrical dimensions on the electrical power and voltage of the harvester. [ABSTRACT FROM AUTHOR]

• A novel composite tube with auxetic honeycomb filler is proposed. • The mechanical properties, deformation characteristics, and fracture modes of three specimens are investigated under three-point bending. • The auxetic honeycomb-filled composite tube exhibits better ductility and a lower degree of load drop after the occurrence of fracture. • The energy absorption performance of the composite tube is optimized by the method of multi-objective optimization. Compared to traditional materials, auxetic materials possess superior bending resistance and energy absorption properties due to their special deformation mechanism. To take advantage of these desirable properties, a novel composite tube with auxetic honeycomb filler was proposed in this work. The honeycomb filler of the composite tube was manufactured by 3D printing technology. The bending properties of two kinds of tubes were studied, namely aluminum tube with re-entrant honeycomb filler and aluminum tube with hexagonal honeycomb filler, respectively. The mechanical responses, deformational characteristics, and failure mechanism of the composite tube under three-point bending were studied by experimental and numerical methods. The study showed that the experiment and numerical results match well with each other. In addition, parametric analysis was carried out to examine the effects of filler and aluminum alloy tubes on the bending properties of the composite tube. Finally, kriging model and the non-dominated sorting genetic algorithm (NSGA-Ⅱ) are used to optimize the design of composite tubes, and the parameter solution with better energy absorption capacity is obtained. [ABSTRACT FROM AUTHOR]

[Display omitted] Natural materials with hierarchical structures usually have superior mechanical properties. Herein, inspired by the macro–micro coupling deformation characteristics of biomaterials, novel hierarchical auxetic-hexagonal honeycombs (AuxHex) metamaterials with various substructures, including equilateral triangles and double arrowheads lattice cells, were constructed. A universal analysis model of the plastic collapse stress was first established, considering the deformation behavior of both the primary and secondary structures. This mechanism-based method gets rid of redundant numerical fitting parameters, and is applicable to different hierarchical lattice structures. Typical hierarchical AuxHex specimens were prepared using selected laser melting and stainless steel. In-plane compression tests and finite element simulation results demonstrated that, in contrast to the regular structures, hierarchical honeycombs exhibit enhancement in their load-bearing capacities and energy absorption ability. The specific modulus of T-AuxHex and A-AuxHex were increased by about 180% and 45%, the specific strength rose by approximately 50% and 15%, and the specific energy absorption was improved by about 160% and 50%. The effects of geometrical parameters were systematically discussed to reveal the mechanisms underlying the enhancement of the above mechanical characteristics. The proposed theoretical model provides a new method for designing the mechanical properties of hierarchical metamaterials by tailoring the type and distribution of secondary structures. [ABSTRACT FROM AUTHOR]

• Hexachiral honeycomb metamaterial with low-frequency vibration isolation and load-bearing capacity is proposed. • The mechanical properties and band gap characteristics are analyzed by both numerical simulation and experiment. • Extreme low frequency band gap (normalized frequency Ω = 0.0043) is obtained. • The influences of structural topology parameters on the mechanical properties and band gap characteristics are discussed. Due to the characteristics of light weight, high specific strength, and excellent damping, auxetic honeycomb structures recently attracted widespread attention. The novel structure with low-frequency vibration isolation and load-bearing capacity became one of the current research hotspots through the improved lattice topology design and associated parameters. For this reason, the authors proposed an auxetic hexachiral acoustic metamaterial with an internal resonant unit. The mechanical properties and band gap (BG) characteristics were analyzed using the finite element method (FEM), and the numerical results were further verified experimentally. Furthermore, the influences of lattice topology parameters on the performance of the above-listed aspects were discussed. Results have shown that the novel metamaterial with extreme low-frequency elastic wave BG and improved mechanical properties can be obtained by combining the hexachiral frame with the internal local resonance unit. [ABSTRACT FROM AUTHOR]

A review of the literature reveals a dearth of works on functionally graded material sandwich shells having an auxetic core layer. This study contributes an analytical approach for the free vibration analysis of doubly curved stiffened sandwich shells with the face sheets of functionally graded materials and the core layer of the auxetic honeycomb material. The theoretical formulation is established based on first-order shear deformation theory associated with the smeared stiffener method. The free vibration solution of simply supported shallow shells with the rectangular platform is derived using Navier's form. The proposed methodology is general and can be applied to examine the natural frequencies of various shell types, including flat, cylindrical, spherical, and hyperbolic paraboloidal panels. Numerical results indicate that the fundamental frequency is largely influenced by the relative proportion of the constituent materials of the face layers, the geometrical parameters of the auxetic honeycomb core layer, as well as the stiffeners. Additionally, a simple optimization technique based on Rao algorithms is introduced to obtain the maximum fundamental frequency of the shell. It is shown that the shell parameters, particularly the thickness of the auxetic core and the number of stiffeners, can be tailored to maximize the natural frequency. Moreover, the optimal solutions are fully dependent on the material proportion of the functionally graded material, the geometry of the shell, and the geometrical parameters of the auxetic honeycomb core. • Free vibration of doubly curved stiffened sandwich shells with FGM faces and auxetic core is freshly addressed • Simple optimization technique based on Rao algorithms is introduced to obtain the maximum fundamental frequency of the shell • New parametric studies on the frequencies of doubly curved stiffened auxetic sandwich FGM shells are examined [ABSTRACT FROM AUTHOR]

[Display omitted] • Bio-inspired, helically oriented tubular structures with tunable deformability and energy absoption efficiency are designed and fabricated. • Helically oriented tubular structures with low helix anlges exhibit auxetic behavior while those with higher helix angles show global buckling under compression. • The helically oriented tubular structures possessed maximum energy absorption efficiency superior or comparable to conventional honeycomb structures. • Mechanical properties and deformation mechanisms of helically oriented tubular structures are predicted and elucidated by finite element simulations. This study designs a series of helically oriented tubular structures inspired by Bouligand-type natural materials to optimize their mechanical performance. Thermoplastic polyurethane-based helically oriented tubular specimens are fabricated by 3D printing and their mechanical properties and energy absorption efficiency under compression are investigated. An auxetic behavior with a negative Poison's ratio is observed for specimens with low helix angles (0°–12°), while specimens with higher helix angles (30°–90°) exhibit a typical buckling behavior and those with intermediate helix angles (13.85°, 16.36°) demonstrate a hybrid helical-like buckling mechanism. Finite-element simulations are performed to elucidate the deformation behaviors and stress distributions under compression. Experimental results show that the helically oriented tubular samples with 90° helix angles yield maximum energy efficiency and compressive strength of 440% and 124%, respectively, higher than for the helically oriented tubular samples with 0° angles. Cyclic tests further show that the 0° sample can almost recover to its original shape, while cracks and delamination are observed for the 30° sample after 200 cycles. The bio-inspired helically oriented tubular structures designed in this study can be applied in engineering, requiring lightweight and energy absorption performance. [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]

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]