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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]

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]

In this paper, the energy absorption capacity of continuous fiber-reinforced thermoplastic auxetic structures is examined experimentally and the results compared with both numerical and analytical methods. To this extent, a 3 D printing technology of Fused Deposition Modeling (FDM) is implemented for fabricating the auxetic honeycombs and quasi-static compression test is conducted to extract the load-displacement behavior of the structure. Both hollow and foam filled lattice structures are tested, and the results revealed that the absorbed energy increased by 20% for PLA and 70% for PA specimens, when using foam. Finite element analysis is also performed using the explicit solver. The onset of failure is determined using the maximum stress criterion and VUSDFLD subroutine and the damage growth is modeled by decreasing the mechanical properties of the elements. The obtained results are in relatively good agreement with the experimental analysis. In addition, a theoretical formulation is developed and the probabilistic analysis is performed to draw the honeycomb failure design envelope, which is a practical tool for designing of various honeycomb configurations. The failure envelope shows that decreasing the strut angle increases the honeycomb failure load, however, the auxetic property of the structure decreases. [ABSTRACT FROM AUTHOR]

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

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]

An analytical method is proposed to determine the displacements of a composite cylindrical shell with auxetic honeycomb core layer and variable thickness under combined axial, internal, and external pressures. The thickness and pressure profiles can be arbitrary continuous functions. The displacements are defined in the framework of the first-order shear deformation theory. The composite shell consists of three layers, in which the inner and outer layers are isotropic and the core layer is made of an auxetic honeycomb material. The constitutive equations obey the Hooke law. The equilibrium equations which are a system of coupled differential equations with variable coefficients are extracted by employing the virtual work principle, and they are solved using the matched asymptotic expansion method of the perturbation technique. The effects of different parameters such as the geometry, honeycomb structure parameters, different load profiles, and the thicknesses on the results are studied. The results are compared with the finite element method and some other references. [ABSTRACT FROM AUTHOR]

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

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

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

• 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]

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]

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

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]

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

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

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

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

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

The paper describes a vibroacoustics analysis of auxetic gradient honeycomb composite structures with hexagonal configurations. We examine two classes of gradient cellular layout – one with continuously varying internal cell angle, the other with gradient cell wall aspect ratio across the surface of the honeycomb panel. The structural dynamics behaviour of the two gradient honeycomb configurations is simulated using full-scale Finite Elements and Component Mode Synthesis (CMS) substructuring. Samples of the gradient honeycombs have been manufactured by means of 3D printing techniques, and subjected to modal analysis using scanning laser vibrometry. We observe a general good comparison between the numerical and the experimental results. A numerical parametric analysis shows the effect of the gradient topology upon the average mobility and general vibroacoustics response of these particular cellular structures. [ABSTRACT FROM AUTHOR]

The impact response of the re-entrant auxetic honeycomb is studied by simulating its in-plane dynamic crushing with FE methods. The characteristics of the peculiar crushing patterns and modes in the re-entrant honeycomb are described. The energy absorption performances of the re-entrant auxetic honeycomb and the hexagonal honeycomb are compared. When subjected to the same magnitude of crushing strain, the re-entrant honeycomb can dissipate more energy through plastic deformation. But if the peak stress is the primary concern for the packaging material, the re-entrant structure tends to generate higher stress in order to dissipate the same amount of impact energy. Moreover, the structural irregularity of the re-entrant auxetic honeycomb is defined and its influence on the dynamic crushing is studied. Unlike the hexagonal honeycomb, the irregular re-entrant auxetic honeycomb can absorb more energy than the regular one in the quasi-static regime. This situation reverses under high speed impact. This study will help to understand the dynamic behavior of the re-entrant foam and provide references for its application. [ABSTRACT FROM AUTHOR]

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

Auxetic metamaterials have generated a great deal of interest in recent years. In this letter, a novel approach which can be used to produce such auxetic metamaterials is presented. This method involves the introduction of patterned slit perforations within a sheet/block of material in order to create systems which resemble a large variety of auxetic systems ranging from rotating units to chiral honeycombs. These perforated systems have also been shown to have the potential to exhibit giant negative Poisson's ratios. (© 2015 WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]

Auxetic materials exhibit a unique characteristic due to the altered microstructure. Different structures have been used to model these materials. This paper treats a development of finite element model and theoretical formulation of 3D star honeycomb structure of these materials. Various shape parameters of the structural cell were evaluated with respect to the basic mechanical properties of the cell. Finite element and analytical approach for various geometrical parameters were numerically used to formulate the characteristics of the material. The study aims at quantifying mechanical properties for any domain in which auxetic material is of interest for variations in geometrical parameters. It is evident that mechanical properties of the material could be controlled by changing the base wall angle of the configuration. The primary outcome of the study is a design guideline for the use of 3D star honeycomb auxetic cellular structure in structural applications. [ABSTRACT FROM AUTHOR]

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

The low in-plane modulus of honeycombs may be used for compliant structures with a high elastic limit while maintaining a required modulus. Numerical and finite element (FE) studies for a functional design of honeycombs having a high shear strength, (τpl*)12 and a high shear yield strain, (γ pl*)12 are conducted with two material selections--mild-steel (MS) and polycarbonate (PC) and five honeycomb configurations, when they are designed to be a target shear modulus, G12* of 6.5 MPa. A numerical study of cellular materials theory is used to explore the elastic limit of honeycombs. FE analysis is also employed to validate the numerical study. Cell wall thicknesses are found for each material to reach the target G12* for available cell heights with five honeycomb configurations. Both MS and PC honeycombs can be tailored to have the G12* of 6.5 MPa with 0.1-0.5 mm and 0.3-2.2 mm cell wall thicknesses, respectively, depending on the number of vertical stacks, N. The PC auxetic honeycomb with θ= -20 deg shows high shear flexibility, when honeycombs are designed to be the G12* of 6.5 MPa; a 0.72 MPa (τpl*)12 and a 13% (γpl*)12. The authors demonstrate a functional design with cellular materials with a large design space through the control of both material and geometry to generate a shear flexible property. [ABSTRACT FROM AUTHOR]

Auxetic cellular structures with outstanding mechanical performance and unique deformation characteristics have a variety of potential applications in aerospace, as ultralight load-bearing structures and vibration isolation structures. Herein, the in-plane compression behaviors of hybrid honeycomb metastructures, comprised of conventional and auxetic honeycombs, are systematically studied by using theoretical calculations, experimental characterization and numerical simulations. The theoretical formulae of elastic modulus and ultimate strength of the architected metastructure are derived by establishing stress analysis models. Three types of hybrid honeycomb metastructures are manufactured by selective laser melting (SLM) with 304 stainless steel. Finite element analysis is performed to unveil the deformation mechanism and failure modes. The theoretical prediction results of elastic modulus and ultimate strength are consistent with simulations and experimental results. In addition, the influences of panel and layer numbers on the mechanical behavior of hybrid honeycomb metastructures are discussed in detail. The results reveal that a hybrid metallic honeycomb metastructure, with stable and superior compressive properties, can be obtained by combining two types of cellular cells, i.e., conventional and auxetic honeycombs. These results provide a baseline for further research and development of novel metastructure designs. [ABSTRACT FROM AUTHOR]

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