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• A cost-effective fabrication method is proposed. • More pronounced NPR effects can be attained by implemented misplaced design. • The comparative method of specific plateau stress is proposed. • The optimized MRHC structure possesses an excellent energy absorption performance. Two-stage plateau stress structures have emerged as a novel research focus in the field of impact protection and energy absorption. The proposal of structures exhibiting a two-stage plateau stress region is increasingly prevalent. However, the majority of currently available two-stage plateau stress structures are predominantly fabricated using 3D printing technology, which can incur substantial costs. Additionally, the majority of currently proposed two-stage plateau stress structures exhibit diminished plateau stress values and possess limited capabilities for energy absorption. The objective of this study is to develop an economically viable metamaterial that exhibits dual high-level plateau stresses and demonstrates exceptional energy absorption capabilities in two in-plane directions. Based on the concept of misplaced design and traditional reinforced honeycomb structures (RHC), a novel metamaterial named misplaced reinforced-honeycomb (MRHC) has been developed. Aluminum alloy component and stainless stee component are fabricated. After the implementation of the misplaced design, the MRHC structure exhibits a pronounced enhancement in negative Poisson's ratio effect. The influence of misplaced design on the mechanical performance of the MRHC structure, as well as the impact of horizontal cell wall length (l 3) and rotation angles (α and β), has been investigated. The multi-objective optimization has been employed to determine the optimal rotation angles α and β. The optimized MRHC structure was compared to the previously proposed two-stage plateau stress structures, revealing its superior energy absorption capabilities in both the in-plane X and Y directions. The proposed MRHC structure exhibits promising potential for future applications in impact buffering and collision protection fields. [Display omitted] [ABSTRACT FROM AUTHOR]

• Three novel lattices by inserting honeycomb struts into the traditional 3D auxetic structure were proposed. • The tensile and compressive mechanical behaviours of hybrid lattices were studied and compared. • 3D hybrid lattices are more effective in tension-dominated applications. Lattice structures have the potential for application in tensile conditions. However, limited studies have addressed tensile behaviours of such structures and compared them with their compressive behaviours. In this paper, re-entrant structure as the foundation was selected to develop new 3D hybrid auxetic honeycomb lattice structures, each characterized by a unique unit cell configuration that features interconnected centre auxetic honeycomb, differentiating it from 2D hybrid auxetic honeycomb structures. A series of uniaxial quasi-static tensile and compressive tests, followed by simulations were conducted on these structures to investigate and compare their energy absorption characteristics. The results show that there were significant differences between these structures in terms of their mechanical behaviours under tension and compression. Especially, the smallest value of energy absorption under tensile load was 86% higher than the largest value under compressive load. The stiffnesses of these lattice structures under tensile loading were about 84–122 times of those of the identical corresponding structures when they were compressed. Meanwhile, the progressive stretching, buckling and collapse mechanisms observed in these structures exhibited excellent stiffnesses and energy absorptions under tensile and compressive load compared to traditional 3D auxetic as the basic structure. The outer frame structure of lattice structures had a direct influence on Poisson's ratio. The work indicates that the stiffness and energy absorption of the traditional 3D auxetic structure can be enhanced by embedding auxetic and honeycomb umbrella shaped elements. [Display omitted] [ABSTRACT FROM AUTHOR]

• A novel EARE is designed by introducing an elliptical annular into RE cell. • EARE produces extra vertical support without hindering lateral deformation. • EARE concurrently enhances auxetic performance, stiffness, and SEA. • Adjusting geometric parameters rationalizes designing mechanical properties. Auxetic structures have sparked a lot of interest due to their excellent mechanical characteristics and unusual negative Poisson's ratio influence. However, the large porosity property results in low stiffness, which limits their application scope. Current approaches to augment stiffness often result in diminished auxetic performance. Therefore, it is challenging to simultaneously enhance the auxetic, stiffness and energy absorption capacity of auxetic structures. To address this issue, this paper proposes a novel elliptical annular re-entrant honeycomb (EARE) by introducing an elliptical annular structure into a conventional re-entrant honeycomb (RE) cell, which can provide extra longitudinal support without hindering lateral deformation. The plateau stress, Poisson's ratio and energy absorption properties of the EARE are investigated by quasi-static compressive tests and finite element modeling. The results show that the EARE honeycomb has two plateau stages due to the supporting effect of the elliptical annular structure. Compared with the conventional RE honeycomb with the same wall thickness, the EARE honeycomb not only exhibits a stronger auxetic effect embodied in the Poisson's ratio reduced by 5.19%, but also has a higher average plateau stress and a higher specific energy absorption of 171.63% and 28.03%, respectively, which significantly improves the stiffness and energy absorption performance. The parameterized analysis reveals that by appropriately adjusting the geometric parameters, the stiffness, energy absorption, and auxetic effect of the EARE honeycomb can be enhanced. The research findings address the conflict between auxetic performance and honeycomb stiffness, providing new insights into the optimization of honeycomb structure design. [Display omitted] [ABSTRACT FROM AUTHOR]

• Novel REAT honeycomb structure derived from bio-inspired gradient-based distribution. • Extensive experiments were conducted to decipher different stages of compression and mechanical properties. • Discovery of a new driver for deformation based on the difference in negative poisson's ratio between layers. • Uncovered 80% higher elastic stiffness and 20% larger densification strain for Chiral-based gradient distribution than its conventional counterpart. • Early-stage compression demonstrated 60% more plateau stress and constant 25% higher energy absorption efficiency. This study focuses on the nature-inspired gradient-based approach to re-designing re-entrant anti-trichiral (REAT) honeycombs through extensive experimental quasi-static compression. Novel perspectives on REAT honeycomb are offered through the introduction of gradient distributions on two critical geometrical parameters, the cylindrical diameter (chiral) and height of the unit cell, rather than the traditional thickness-based gradient approach. Chiral-based gradient approach demonstrated clear advantages in elastic stiffness, specific energy absorption (SEA) and densification strain over uniform REAT structures of constant geometrical parameters. These advantages are exhibited in their extended and constantly increasing quasi-plateau stage, consistent specific energy absorption (SEA) especially during early stages of compression, and most importantly, the ability to maintain a relatively constant energy absorption efficiency that is 25% more than that of the Base uniform REAT structure. Height gradient-based REAT structures, on the other hand, were able to leverage on associations between the negative Poisson's ratio (NPR) effect and height of unit cell to demonstrate notable deformation patterns across various portions of the structure. The present work reveals the performance enhancements through alternative gradient-based approaches over thickness-based gradient approaches and highlighted the differences in NPR between layers as the main driver of compressive collapse apart from the commonly concluded difference in relative density. [Display omitted] [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]

• 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 novel Diabolo shaped honeycomb based on re-entrant hexagonal honeycomb is proposed. • Four enhanced honeycombs are designed based on the Diabolo shaped honeycomb by adding horizontal or longitudinal ribs. • The simulation results show that Diabolo shaped honeycomb has better impact resistance and energy absorption than re-entrant hexagonal honeycomb. • The plateau stress and specific energy absorption of the honeycomb are significantly influenced by the geometric parameters. This paper presents the design of a novel Diabolo shaped honeycomb (DSH) based on re-entrant hexagonal honeycomb (RHH), and four enhanced honeycombs are designed based on the DSH by adding horizontal or longitudinal ribs. The finite element software ABAQUS/EXPLICIT is applied to investigate the relationship between crashworthiness and energy absorption performance with different impact velocities and geometric parameters. The simulation results show that DSH has better impact resistance and energy absorption than RHH. DSH has improved plateau stress by 141.3%, 78.7%, and 22.7% of low-velocity, medium-velocity, and high-velocity compression, respectively, and SEA by 103.7%, 79.3%, and 7.3%, respectively. In addition, the impact resistance of the four enhanced honeycombs is further improved. The shrinkage effect of DSH after impact is not as good as that of RHH, and the horizontal ribs suppress the negative Poisson's ratio property of the honeycomb. Different impact velocities affect the deformation pattern of the honeycomb. With the increase of impact velocities, the honeycomb has a transition from overall deformation to local deformation with increasing velocity. The plateau stress and specific energy absorption of the honeycomb are significantly influenced by the geometric parameters. This research provides a reference for the optimal design and application of honeycombs as energy absorbing components. [Display omitted] [ABSTRACT FROM AUTHOR]