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• 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]

• 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]

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]

• 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]

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]

• 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 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]

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]

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]