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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]

In this paper, the thermal shock resistance of an auxetic ceramic honeycomb plate is studied based on the fracture mechanics concept for the cases of a central crack or an edge crack. The transient temperature field and transient thermal stress field are obtained for both auxetic and non-auxetic structures. The relationship between the thermal stress intensity factor (TSIF) and the internal cell angle, crack length and time is determined and the critical temperature for the initiation of crack propagation is predicted. Results show that compared with the non-auxetic ceramic honeycombs which are at an internal cell angle of 30°, the critical temperature of the auxetic ceramic honeycombs whose cell are orientated at an angle of −30° increases by 78.5% and the TSIF at the crack tip decreases by 40%, respectively. Hence, the auxetic structures have better thermal shock resistance. This study indicates that auxetic ceramic honeycombs have significant potential applications in harsh temperature environments. [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]

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]

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

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

• The proposed hybrid AuxHex structure consists of auxetic and honeycomb cells. • The equations for modulus and strength along x - and y -directions are derived. • Theoretical results are in agreement with simulation and experimental results. • Mechanical properties and specific energy absorption are enhanced 16% and 38%. The architected mechanical metamaterials have garnered significant research attention for a variety of engineering application due to their remarkable mechanical properties and unique deformation behavior. Herein, the in-plane uniaxial compressive response and energy absorption capacity of a novel hybrid configuration, AuxHex structure, which consists of auxetic and hexagonal honeycomb cells, are systematically investigated through theoretical, finite element simulation and experimental methods. A series of AuxHex sandwich core panels have been fabricated with nylon material by using additive manufacturing route. The relationships for Young's modulus and plastic collapse stress along different loading directions are derived and validated through the comparative analysis. In addition, the deformation mechanism and failure modes of the AuxHex structure have also been discussed in detail. The AuxHex structures have exhibited superior Young's modulus, collapse strength and energy absorption than traditional honeycomb structures. In the x -direction, the energy absorption capacity was improved by 38%, which can be attributed to the uniform and stable deformation mode of the unit cell. The theoretical prediction results of Young's modulus and plastic collapse stress are consistent with finite element simulation and experimental results. The AuxHex structures demonstrate a novel design strategy for the architected metamaterials through the combination of various cellular cells. The hybrid structures will play an important role in both the load-bearing and energy-absorbing applications, and it demonstrates a novel design strategy for the architected metamaterials through the combination of various cellular cells. Image, graphical abstract [ABSTRACT FROM AUTHOR]

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

Abstract Recently, auxetic honeycombs have attracted considerable attention for their excellent mechanical properties, especially the potential applications for energy absorption. In this paper, a novel re-entrant auxetic honeycomb is proposed and named as re-entrant star-shaped honeycomb (RSH), with the in-plane impact responses explored theoretically and numerically. Three types of microstructural deformation modes are observed under different impact velocities, including low-velocity mode, medium-velocity mode and high-velocity mode. Moreover, a deformation map is summarized to illustrate the effects of the impact velocity and the relative density on the deformation modes. Two typical plateau stress regions are detected under low-velocity impact loading, and the second plateau stress is almost twice higher than the first one. The transverse contraction of the RSH mainly occurs at the first plateau region, which is different for the classical re-entrant honeycomb (RH). In addition, the absorbed energy of the RSH decreases slightly and then increases with the impact velocity. The results of the finite element simulations suggest that the RSH shows more excellent impact resistance, compared with the RH and SSH with same cell wall thickness. Furthermore, the effects of the cell wall thickness and the impact velocity on the crushing strength of the RSH are discussed, and the theoretical results are in good agreement with the finite element simulations. [ABSTRACT FROM AUTHOR]

Abstract This paper mainly concerns effects of the auxetic structure on the crash performances in terms of the axial crash force, specific energy absorption, and deceleration, which are evaluated with the conventional and honeycomb structures. Based on the systematic design procedure, the re-entrant units for the auxetic structure are regularly arranged in the tube wall, which are produced by the additive manufacturing with SUS316L metal powder. Under the low impact condition, the auxetic does not only exhibit higher specific energy absorption, but also demonstrate substantially low deceleration due to effect of the densification during the axial crash compared with the conventional tube. Furthermore, while the honeycomb tube demonstrates oscillating behavior in the deceleration, the auxetic tube tends to maintain steady deceleration after the first peak during the axial crash, which is able to guarantee enhanced damping performances under the low impact condition. [ABSTRACT FROM AUTHOR]

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

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

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]

In this study, some new 2D auxetic metamaterials were investigated and called octagonal auxetic metamaterials. The structures were examined by numerical and experimental approaches and 3D printing additive manufacturing technique was employed to fabricate the structures from thermoplastic polyurethane elastomer (TPU) which is considered as a hyperelastic material. Auxetic behavior was caused by adding small triangles and squares to the vertices of the octagonal structure and applying high compressive strain. Although the octagonal structure showed negative Poisson's ratio at high compressive strain, the results suggested that adding triangles to the vertices of the octagonal structure as well as increasing the triangle edge length led to higher negative Poisson's ratio. In contrast, with small squares adding to the vertices of the octagonal structure, Poisson's ratio became slightly more negative. In addition, by increasing the square edge length, Poisson's ratio measured near zero or even positive values. Moreover, a parametric study was carried out by Python 3.6.5 programming language to find the best triangle and square edge length which caused the most auxeticity. [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]

The main goal of this study is using analytical solution to investigate the nonlinear dynamic response and vibration of sandwich auxetic composite cylindrical panels. The sandwich composite panels have three layers in which the top and bottom outer skins are isotropic aluminum materials, the central auxetic core layer – honeycomb structures with negative Poisson's ratio using the same aluminum material. The panels are resting on elastic foundations and subjected to mechanical, blast and damping loads. Based on Reddy's first order shear deformation theory (FSDT) with the geometrical nonlinear in von Karman and using the Airy stress functions method, Galerkin method and 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 Winkler and Pasternak foundations, mechanical, blast and damping loads on the nonlinear dynamic response and the natural frequencies of sandwich composite cylindrical panels are studied. [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]

Auxetic materials exhibit many superior properties but drawback in low stiffness owe to the substantial porosity. Some narrow-ribs enhanced auxetic honeycombs have been designed for improving the in-plane stiffness. For these narrow-ribs enhanced auxetic structures, local buckling likely appears as the reinforcing walls are designed in low thickness for superior auxeticy. In this paper, a novel narrow-ribs enhanced auxetic honeycomb is designed by embedding rhombus into each cell of the normal re-entrant hexagonal honeycomb (NRHH). Analytical model is built to investigate the elastic behaviors of the new proposed honeycomb under uniaxial compression, in which the incremental method is firstly introduced for post-local-buckling analysis. Numerical simulations are carried out to verify the analytical results. It is interesting that bilinear elastic characteristic is found for the stress-strain and transverse strain-longitudinal strain curves of the new proposed honeycomb on account of the local buckling. Parameters studies are performed and the new proposed honeycomb is proved to exhibit superior mechanical properties compared to other narrow-ribs enhanced honeycombs. Significantly, the incremental method brought forward in the present paper for the local buckling analysis can be popularized to other honeycombs enhanced with narrow-ribs. Thus, the bilinear elastic characteristic is a general feature for these honeycombs. [ABSTRACT FROM AUTHOR]

Honeycomb structures have been used extensively in lightweight sandwich structure and impact energy absorption applications. Recently the research has been carried out on auxetic honeycombs that have negative Poisson's ratio (NPR). Auxetic structures are attractive for various engineering applications because of their unique mechanical properties, volume change control and excellent impact energy absorption performance. In this study, novel design and performance improvement of new auxetic-strut structures were presented. A comparative study of in-plane uniaxial compression loading behavior of regular honeycomb, re-entrant auxetic honeycomb, locally reinforced auxetic-strut structure and a hybrid structure of combining regular honeycomb and auxetic-strut structure was conducted on 3D printed samples. The deformation and failure modes of the different cells were studied and their performance was also discussed. The new auxetic-strut structure showed better mechanical properties than the honeycomb and auxetic structure. For example, the compressive strength of the auxetic-strut design is ~ 300% more than that of honeycomb structure and ~ 65% more than that of auxetic structure. With lower values of the Poisson's ratio, the new design can absorb more energy when compared to the other structures. Hybrid structure of auxetic-strut and honeycomb cells allows us tailor the deformation paths to provide desired failure modes. [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]

• 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]