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• 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]

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

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

• 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]

• Metallic graded RECH prototypes fabricated through a low-cost step-by-step method. • Graded RECH takes advantage of structural hierarchy and functional gradient. • Gradient design causes multi-step deformation mode and multi-plateau stress. • Improved SEA and auxeticity of graded RECH under different crushing velocities. As lightweight energy-absorbing materials, auxetic honeycombs have demonstrated promising applications in engineering fields. In this study, the graded re-entrant circular auxetic honeycombs (RECH) were proposed, and their metallic prototypes were fabricated through a low-cost step-by-step method. The novel design of graded RECH takes advantage of structural hierarchy on the meso-scale and functional gradient on the macro-scale. The in-plane crushing behaviors of uniform (U) RECH, positive gradient (PG) RECH and negative gradient (NG) RECH with the same relative density were investigated under different crushing velocities. The finite element (FE) models were validated by comparing against the experimental and theoretical results. The results showed that the gradient design can control the multi-step deformation modes of RECH, which leads to the multi-plateau characteristics and reduced initial stress peaks in stress-strain curves. Under quasi-static crushing, the specific energy absorption (SEA) of PG-RECH is higher by 43.9% than that of U-RECH owing to more plastic deformations of hierarchical circular walls at a large strain. Under dynamic impacts, the SEA of NG-RECH is 2.7 times and 1.5 times those of PG-RECH and U-RECH at a small strain, respectively. Finally, the NG-RECH shows more negative Poisson's ratio (NPR) behavior than the U-RECH under dynamic crushing. This study offers new routes to the fabrication and design of auxetic metamaterials. [Display omitted] [ABSTRACT FROM AUTHOR]

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

Elastic networks model that is used to model a class of two-dimensional cellular structures including re-entrant and regular honeycombs is considered. Two mechanical parameters (longitudinal stiffness and torsional stiffness) are used to describe the interaction between the nodes in a lattice for a given geometry. Effective properties with emphasis on the auxeticy of solid materials corresponding to the considered microstructures are investigated. A method based on comparison of the strain energies at macro- and microscale is proposed to determine the effective properties of continuum and can be applied to other cellular materials. All components of stiffness tensor are determined as functions of interaction parameters. Thus, the general parametric study of the honeycomb structures is made possible. Re-entrant honeycomb structures demonstrate the auxetic properties at any combination of parameters whereas the regular honeycombs can have both positive and negative Poisson's ratios. Comparison with other model shows that the 2-parameter elastic networks can successfully describe isotropic materials. However in cases of higher anisotropy this model can be used within certain limitations. [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]

• A new NPR 2D honeycomb was developed based on the horizontal series-connected parallelograms. • A combination of analytical, numerical and experimental method was adopted to investigated the in-plane effective modulus of the new 2D honeycomb. • Dependence of the mechanical properties of the new 2D homeycomb on the geometric parameters was exploited. • New mechanism for generating NPR was discovered. • The new 2D honeycomb was extended to three dimensions. This paper details a new 2D auxetic honeycomb that was structured by mirroring the horizontal series-connected parallelograms along the vertical direction. A combination of analytical, numerical, and experimental methods was used to gain a deep understanding of the elastic behavior of the new honeycomb and examined its dependence on the geometric parameters. The results showed that the new honeycomb can achieve a negative Poisson's ratio via a novel mechanism. Furthermore, the newly developed 2D honeycomb was extended to three dimensions, and three kinds of 3D structures were conceived via different splicing methods. A preliminary numerical study was conducted to explore the mechanical properties of the 3D structures. An auxetic effect was found in two principal orthogonal coordinate directions of those 3D structures when they were compressed along the other principal axis. This work may provide a new insight into the design of both the 2D and 3D auxetics. [ABSTRACT FROM AUTHOR]