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Auxetic lattice structures are three-dimensionally designed intricately repeating units with multifunctionality in three-dimensional space, especially with the emergence of additive manufacturing (AM) technologies. In aerospace applications, these structures have potential for use in high-performance lightweight components, contributing to enhanced efficiency. This paper investigates the design, numerical simulation, manufacturing, and testing of three-dimensional (3D) star-shaped lattice structures with tailored mechanical properties. Finite element analysis (FEA) was employed to examine the effect of a lattice unit's vertex angle and strut diameter on the lattice structure's Poisson's ratio and effective elastic modulus. The strut diameter was altered from 0.2 to 1 mm, while the star-shaped vertex angle was adjusted from 15 to 90 degrees. Laser powder bed fusion (LPBF), an AM technique, was employed to experimentally fabricate 3D star-shaped honeycomb structures made of Ti6Al4V alloy, which were then subjected to compression testing to verify the modelling results. The effective elastic modulus was shown to decrease when increasing the vertex angle or decreasing the strut diameter, while the Poisson's ratio had a complex behaviour depending on the geometrical characteristics of the structure. By tailoring the unit vertex angle and strut diameter, the printed structures exhibited negative, zero, and positive Poisson's ratios, making them applicable across a wide range of aerospace components such as impact absorption systems, aircraft wings, fuselage sections, landing gear, and engine mounts. This optimization will support the growing demand for lightweight structures across the aerospace sector. [ABSTRACT FROM AUTHOR]

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

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

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

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

Due to their superior structural and mechanical properties, materials with negative Poisson's ratio are of increasing interest to research scholars, especially in fuel-efficient vehicles. In this work, a new concave I-shaped honeycomb structure is established by integrating the re-entrant hexagon and the I-shaped beam structure, and its negative Poisson's ratio characteristics and energy absorption properties are investigated. The effect of structural parameters on the energy absorption characteristics is analyzed using the finite element model. The results show that both the specific energy absorption and peak impact force decrease with the increase in cellular length and vertical short cellular height, and increase with the increase in horizontal short cellular length and cellular thickness. To obtain a smaller peak impact force and larger specific energy absorption with smaller mass, the four cell sizes were optimized by using Latin hypercube sampling, Gaussian radial basis function, and non-dominated sorting genetic algorithm II (NSGA-II). Compared with the original design, the SEA increased by 44.175%, and the PCF increased by 25.857%. Meanwhile, the mass decreased by 31.140%. Hence, the optimal structure has better crashworthiness. [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]

• 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]

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

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

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

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

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]

• 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]

• A novel re-entrant auxetic honeycomb metamaterial with zigzag inclined ligaments is proposed. • The proposed metamaterial can be conveniently fabricated by low-cost traditional manufacturing。 • Theoretical formulae for the effective elastic constants of the proposed metamaterial are developed. • The proposed metamaterial possesses tailorable mechanical properties. Conventional two-dimensional (2D) re-entrant auxetic honeycomb is one of the earliest examples of auxetic metamaterials. Recently, plenty of 2D re-entrant honeycomb variants are developed to enhance their stiffness. However, the stiffness enhancement for most of the existing designs is generally obtained with compromising the conjugated auxeticity. Moreover, most of the existing designs are hard to be fabricated by low-cost traditional manufacturing technology due to their complex architectures. The present work aims to enhance the stiffness without compromising the conjugated auxeticity, and yet retains its convenience and low-cost for fabrication. By introducing zigzag inclined ligaments, a novel 2D re-entrant auxetic honeycomb metamaterial is firstly proposed. Based on Castigliano's second theorem, a theoretical model of the proposed design is established to facilitate the understanding of the underlying microstructural mechanisms. The obtained analytical solutions, as validated by systematic finite element (FE) analyses, elucidate different roles of the microstructural geometry on the effective mechanical properties of the proposed re-entrant auxetic honeycomb metamaterial. Compared with the conventional re-entrant auxetic honeycomb, which is a particular case of the present design, both the stiffness and the auxeticity along specific principal directions of the present design are improved remarkably. [ABSTRACT FROM AUTHOR]

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

• A simple re-entrant auxetic metamaterial is designed by rotating and connecting 2D re-entrant honeycomb cells. • The energy absorption of the proposed metamaterial is discussed under different design parameters. • The proposed 3D re-entrant auxetic lattice has desirable stiffness and specific energy absorption. • The initial peak stress and energy absorption capacity of the metamaterial can be adjusted via changing design parameters. As a branch of auxetics, the re-entrant hexagonal honeycomb has many superior mechanical performances. However, most research focused on two-dimensional (2D) re-entrant structures or three-dimensional (3D) structures without high compressibility. The energy absorption capacity of such structures is deficient for practical applications. Therefore, it is important to investigate the 3D re-entrant honeycomb structures which can sustain large deformation in order to make the most use of the materials. In this work, a simple 3D re-entrant unit cell is designed, manufactured and examined. The influence of geometric parameters on the deformation mode and energy absorption capacity is investigated numerically. The experimental results are in good agreement with the finite element prediction. The proposed 3D re-entrant auxetic metamaterial not only possesses a greater bearing capacity but also presents a stable compression deformation. The structure exhibits a desirable energy absorption behavior, including obvious auxetic behavior and a long stress plateau. By adjusting the geometrical parameters of the structure, the performances of energy absorption and compression stiffness can be improved. These findings provide a new idea to design 3D auxetic metamaterials and promote their utilization in protective structures. [Display omitted] [ABSTRACT FROM AUTHOR]

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

This paper assesses the thermal shock behaviors of the auxetic honeycomb layer (HL) through consideration of crack propagation and new crack initiation. All material properties are temperature-dependent. To calculate the thermal stress field with no crack, the finite difference approach is used. On this basis, a theoretical model for thermal stress intensity factor and thermal stress between cracks is developed. The model combines the equivalent fracture toughness and equivalent tensile fracture strength as the failure criteria. The critical temperature for crack propagation and new crack initiation in the HL is determined. The results reveal that the thermal shock resistance (TSR) of the HL is overestimated if the temperature-dependent material properties (TDMPs) are not taken into account. Multiple cracking can dramatically improve the TSR of the HL. Compared to the non-auxetic HL, the TSR of the auxetic HL is significantly enhanced. Furthermore, the HL with lower relative density generally possesses higher TSR, and the corresponding physical mechanisms are revealed. • Thermal shock resistance of auxetic honeycomb layer is assessed considering multi-cracking. • Thermal shock resistance is overestimated if temperature dependence of material properties is ignored. • Multiple cracking increases the thermal shock resistance of the structure. • Auxetic property improves the thermal shock resistance well. [ABSTRACT FROM AUTHOR]

This work proposed an improved modification on the common re-entrant hexagonal honeycomb (RHH) by replacing the solid junction of the cell walls with a small hollow circle, and thus achieving a novel kind of honeycomb. A simple energy-based approach was adopted to develop theoretical models for predicting the in-plane equivalent elastic moduli of the new honeycomb. Finite element analysis was employed to verify the theoretical models and then the effects of the micro geometrical parameters on the in-plane elastic behaviors were further discussed. The results showed that the new honeycomb possesses an obvious negative Poisson's ratio effect, meanwhile, can achieve higher specific Young's modulus and shear modulus than the RHH. Moreover, the new honeycomb was found to exhibit a more tailored anisotropy than the RHH from the off-axial properties analysis. As a result, the new honeycomb may be an effective substitute for the RHH in application and the new layout can be a good guide for the improved design of auxetic honeycombs. [ABSTRACT FROM AUTHOR]

• Nonlinear thermo-buckling and postbuckling analysis. • The imperfect eccentrically stiffened FGM double curved shallow auxetic shells. • The shell subjected to uniform external pressure, axial compressive, thermal loads. • Using analytical method, the FSDT, the Galerkin and stress function methods. • Taking account the effect of pores and temperature-dependent material properties. It is the first time the nonlinear thermo-mechanical analysis (buckling and postbuckling) of imperfect eccentrically stiffened (ES) double curved shallow shells made of auxetic material under uniform external pressure, axial compressive and thermal loads has been studied by adopting analytical method. The double curved shallow sandwich shell is constructed by an auxetic honeycomb core layer with negative Poisson's ratio and two isotropic homogeneous skin layers. In the present study, the outer surface of the structure is reinforced by a system of FGM stiffeners and taking the influence of pores in the stiffeners into account to increase the load capacity of the structure. Besides, the material properties of the shells and stiffeners are both temperature-dependent. The first-order shear deformation theory is applied to derive equilibrium and compatibility equations of double curved shallow auxetic shell, considering both the geometrical nonlinearity in the Von Karman sense and initial geometrical imperfections and shells placed on the Winkler – Pasternak foundation. The Galerkin and stress function methods are proposed to determine the critical load value and the deflection– load curve by taking the root form of the two-term rotation angles to give the Galerkin integral an equilibrium equation. Several comparisons with results in other literature are made to examine the reliability and accuracy of the method used in the present study. Finally, the effects of thermal environment, reinforced stiffeners, elastic foundation, pores and parameters of auxetic core layer on the buckling and postbuckling loads are evaluated in this paper. The numerical and graphical results show that the reinforced stiffeners, auxetic core, temperature and porous distribution have significantly influenced on the buckling and postbuckling loads of ES double curved shallow auxetic honeycomb sandwich shells. [ABSTRACT FROM AUTHOR]

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

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