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AbstractTo enhance the performance of the six-missing rib honeycomb (ASRH), two axisymmetric missing rib honeycombs, ASRH-1 and ASRH-2, are proposed in this study. First, the in-plane impact performance of ASRH, ASRH-1, and ASRH-2 is experimentally compared to verify the accuracy of the finite element model. Then, the deformation patterns, specific energy absorption (SEA), and negative Poisson’s ratio (NPR) effects of the three honeycombs under different parameters were parametrically investigated. The results indicate that ASRH-1 and ASRH-2 exhibit higher SEA than ASRH at an impact velocity of 10 m/s, but the NPR effect does not change significantly. The axisymmetric honeycomb demonstrates no advantage at 50 and 100 m/s high-speed impacts. The Poisson’s ratio effect of the three honeycombs varied greatly with the internal ligament r of the honeycomb. The axisymmetric design offers a new concept for a NPR honeycomb design. [ABSTRACT FROM AUTHOR]

Inspired by rotating rigid structures, an auxiliary rotating triangular honeycomb structure (ARTH) is designed in this article. The structure has dual platform stress, which can reduce the initial peak stress generated during collisions, reducing injuries to pedestrians and vehicle occupants. The accuracy of the finite element numerical model is verified by experiments, and a series of researches are carried out. The mechanical properties of the structure at different velocities are studied and the classification diagram of deformation modes is obtained. Under low‐speed impact load, ARTH has two deformation stages and two stress plateau regions, in which the stress of the second plateau is more than twice that of the first plateau. Then, a theoretical model based on plastic dissipation theory predicts the stress platform at different deformation stages under quasi‐static conditions. Parametric analysis shows that increasing wall thickness t can significantly improve the stress platform and energy absorption, but the negative Poisson's ratio effect is weakened. The influence of angle θ on the first stage deformation of ARTH is significant. These studies can provide some references for the design of double‐platform stress and the reduction of initial peak stress of rotating auxiliary structures. [ABSTRACT FROM AUTHOR]

Here, hexagonal and triangular lattices are layered and merged into a re-entrant honeycomb to replace each cell wall of the re-entrant honeycomb. In order to study the crushing behavior of the new variable-angle-variable-substructure-number-gradient honeycomb, a finite element analysis of in-plane and out-of-plane crushing was carried out. The effects of different gradient parameters on the deformation mode and extrusion response were discussed, respectively. The results show that different grading parameters have different effects on the crushing behavior of honeycombs for in-plane and out-of-plane crushing. Compared with out-of-plane crushing, the influence of the hierarchical structure on the in-plane crushing deformation mode and the increase in platform stress are much larger. Compared with the ordinary honeycombs, changing the substructure angle does not necessarily improve the platform stress of the honeycomb. From the perspective of platform stress, the layered structure has different effects on the improvement of honeycomb energy absorption; the maximum platform stress of the honeycomb is increased. [ABSTRACT FROM AUTHOR]

To investigate the effect of nodal configuration on the mechanical properties of hexachiral honeycombs, three specimens, namely, a standard honeycomb, a thickened-node honeycomb, and a filled-node honeycomb, were prepared using 3D-printing technology. Several quasi-static compression tests were performed, which revealed that nodal reinforcement can inhibit nodal aberrations during ligament winding, thus facilitating the "rotational" mechanism and improving the negative Poisson's ratio properties of the honeycomb. Experiments performed using the finite element method showed that nodal reinforcement mainly played a role in the stage of stress rise, and the role of nodal filling was more significant than that of nodal thickening. Low-strain standard honeycombs presented the highest specific absorption energy. However, the specific absorption energy of the filled-node honeycomb and the thickened-node honeycomb exceeded that of the standard honeycomb at a strain of 0.71. The conclusions presented herein can aid in the optimal design of honeycombs and contribute to the design of protective structures. [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]

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]

This paper presents a modified re-entrant honeycomb auxetic structure. The structure is constructed by adding an additional horizontal member between the vertical and re-entrant member of the semi-re-entrant honeycomb model to increase the overall compliance of the structure in order to obtain higher values of negative Poisson's ratio (NPR). An analytical model of the structure is presented, taking into account the bending, shear, and axial deformations. The model is verified using finite element analysis (FEA) and tensile testing. The results of FEA and tensile testing corroborate the results of the presented mathematical model. The structure is also compared to the existing re-entrant honeycomb structure. The newly added strut has shown a direct effect on the directional properties of the overall structure. With an increase in the newly added strut to re-entrant lengths, NPR was significantly enhanced in the x-direction and reduced in the y-direction loadings. The structure shows an improved Young's modulus compared to solid material in both loading directions, especially for the low values of the new strut and re-entrant lengths ratio. The structure also shows that high NPR can be achieved for low relative density compared to semi re-entrant honeycomb structure. [ABSTRACT FROM AUTHOR]

In this paper, we propose an elliptical anti-tetrachiral honeycombs structure (E-antitet) with in-plane negative Poisson's ratio (NPR) and orthogonal anisotropy. The analytical and numerical solutions of the in-plane Poisson's ratio and Young's modulus are given by theoretical derivations and finite element method (FEM) numerical simulations and are verified experimentally by a 3D printed sample. Finally, we analyzed the influences of different parameters on the in-plane Poisson's ratio and Young's modulus of E-antitet. The results show that the proposed E-antitet can achieve a smaller Poisson's ratio and larger Young's modulus in the desired direction compared with the anti-tetrachiral honeycombs structure (antitet), and moreover, the E-antitet has a more flexible means of regulation than the antitet. The analytical results of this paper provide meaningful guidance for the design of chiral honeycomb structures. [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]

In this paper, we design a new three-dimensional honeycomb with a negative Poisson's ratio. A honeycomb cell was first designed by out-of-plane stretching a re-entrant honeycomb and the honeycomb is built by spatially combining the cells. The in-plane response and energy absorption characteristics of the honeycomb are studied through the finite element method (FEM). Some important characteristics are studied and listed as follows: (1) The effects of cell angle and impact velocity on the dynamic response are tested. The results show that the honeycomb exhibits an obvious negative Poisson's ratio and unique platform stress enhancement effect under the conditions of low and medium velocity. An obvious necking phenomenon appears when the cell angle parameter is 75°. (2) Based on the one-dimensional shock wave theory, the empirical formula of the platform stress is proposed to predict the dynamic bearing capacity of the honeycomb. (3) The energy absorption in different conditions are investigated. Results show that as the impact velocity increases, the energy absorption efficiency gradually decreases. In addition, with the increase of cell angle, the energy absorption efficiency is gradually improved. The above study shows that the honeycomb has good potential in using in vehicle industry as an energy absorption material. It also provides a new strategy for multi-objective optimization of mechanical structure design. [ABSTRACT FROM AUTHOR]

Honeycomb structure containing curved reentrant sides with negative Poisson's ratio (NPR) was designed and the impact dynamics behaviors were studied by finite element method. The Poisson's ratio and the energy absorption capacity of the honeycomb structure with different arc angle were studied under different compression velocities. The results show that the Poisson's ratio of the honeycomb structure can reach −0.373 with arc angle of 180°. The energy absorption capacity of the honeycomb structure increased with an increasing compression velocity, and the deformation mode changed from X type to V type and I type. When the compression velocity is low, the dynamic response curve of the honeycomb structure with arc angle of 180° has the characteristics of two-stage plateau region. When the compression velocity is high, the energy absorption capacity of the honeycomb structure increased with an increasing arc angle. When the arc angle is higher than 120°, the honeycomb structure has NPR effect, and the energy absorption capacity of the honeycomb structure is better than the honeycomb structure with other arc angles. [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]

A star-shaped honeycomb with asymmetric cells is proposed in this paper. The accuracy of the finite element model is verified by experiments, and the mechanical characteristics and deformation modes of the honeycomb are studied by numerical simulation. First, the energy absorption and deformation modes of a star-shaped honeycomb with asymmetric cells were studied under low-, medium- and high-velocity impacts. Second, the influence of different angles and different wall thicknesses on the energy absorption of honeycomb was studied. The results show that model 3 exhibits obvious negative Poisson's ratio characteristics under different impact velocities. As the angle increases, the energy absorption and plateau stress of mode 1 also increase. However, for mode 3, increasing θ can enhance the negative Poisson's ratio, but the specific energy absorption and plateau stress of the structure will decrease. Compared with the traditional star-shaped honeycomb, θ = 50° for mode 1, the specific energy absorption and plateau stress are increased by 21.53% and 13.32%, respectively. With increasing wall thickness, the specific energy absorption and plateau stress were significantly increased. Compared with mode 1 with t = 0.5 mm and mode 1 with t = 0.75 mm, the specific energy absorption and plateau stress increased by 50.51% and 125.56%, respectively. • A star-shaped honeycomb with asymmetric cells (SSHAC) is proposed. • The SSHAC is designed in an axisymmetric manner, with six structures designed in different extension directions. • Compared with traditional star-shaped honeycomb, SSHAC has a more stable deformation mode. • SSHAC provides a certain reference for cells designed with asymmetric elements in symmetrical form. [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]

• 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]

Negative Poisson's ratio honeycombs have been widely studied in recent years due to their unique mechanical properties. A tetrachiral honeycomb (TCH) exhibits a bulging effect when subjected to in-plane impact, reducing its Poisson's ratio effect. To improve the performance of TCH, this study proposes two types of axisymmetric tetrachiral honeycombs (ATCH-1 and ATCH-2). First, the in-plane impact performances of TCH, ATCH-1, and ATCH-2 are compared via experiments, and the accuracy of the finite element model is validated. Then, the effects of the different parameters on the deformation modes, energy absorption characteristics, and negative Poisson's ratio effects of the three types of honeycombs are analyzed via finite element models. ATCH-1 and ATCH-2 have higher specific energy absorption (SEA) and a more significant negative Poisson's ratio effect than TCH at an impact velocity of 10 m/s. However, the axisymmetric honeycombs do not have advantages at impact velocities of 50 m/s and 100 m/s. The cylindrical radius r significantly affects the deformation mode of the three types of honeycombs. The axisymmetric design provides a new concept for the novel negative Poisson's ratio honeycomb design. [ABSTRACT FROM AUTHOR]

It has been demonstrated that origami structures can be successfully used for honeycomb structures. And the excellent energy absorption properties of origami structures make them a promising candidate for use in cushioning when paired with honeycomb structures. Consequently, the honeycomb structure was recreated using origami structures to generate new specimens, aiming to reduce the initial peak force under out-of-plane crushing while maintaining the energy absorption properties. The specimens were created using 3D printing technology, and experiments with quasi-static flat pressing were carried out. The properties of the origami-based honeycomb were investigated during out-of-plane crushing, with an emphasis on its energy absorption properties. Additionally, the compressive properties of the origami-based honeycomb are compared with those of traditional re-entrant honeycomb in z-axial directions. To further investigate the properties of the origami-based honeycomb, a validated model was developed in Abaqus, and the accuracy of the finite element model's forecast was confirmed. The results show excellent lateral material shrinkage under axial compression, which is an obvious negative Poisson's ratio (NPR) effect, and a distinct hardening process with stiffness increases when the origami-based honeycomb structure experiences densification. Moreover, compared to the traditional re-entrant honeycomb structure, the origami-based honeycomb has a lower peak crushing force and a smoother plateau stress curve, making it an ideal material for protective structural applications. Increasing the height H or decreasing the forward length V are effective methods for increasing the structure's specific energy absorption (SEA). Additionally, different configurations will have distinct consequences for the structure. Compared to ordinary origami-based honeycombs, the honeycomb with different configurations has superior energy absorption properties and can also achieve stiffness jumps and segmental self-locking. • Under compression, the origami honeycomb displays an evident NPR and densification effect. • This origami honeycomb can effectively utilize the plastic deformation energy of materials. • Differently arranged origami honeycombs suffer stiffness jumps, enabling deformation control. [ABSTRACT FROM AUTHOR]

This article presents the combination of mixed interpolation of tensorial components technique of triangular elements and the edge-based smoothed finite element method (ES-MITC3) developed on the higher-order shear deformation theory (HSDT). The free vibration behavior of auxetic honeycomb sandwich plates with the functionally graded material (FGM) skin layers generated by the proposed program is trained and predicted by an artificial neural network (ANN) model using Matlab coding for reducing computational time and saving computer resources, the proposed approach is expected suitable for practical engineering problems. The strain field of edge-based smoothed triangular elements is approximated by using the generalized C0-HSDT and Lagrange shape functions. Ultra-light features of sandwich plates are obtained by using the auxetic honeycomb core layer (negative Poisson's ratio) and reinforced by FGM skin layers. The present results are compared with other published studies to verify the accuracy and reliability. Besides, the ANN model is also built to train obtained results and accurately predict the natural frequency of structures without running the code. Moreover, the effects of parameters such as geometrical and material properties (especially the auxetic parameters) on the free vibration behavior of auxetic honeycomb sandwich plates with FGM skin layers are investigated in detail. • An edge-smoothed FEM employing the HSDT is developed for vibration analysis of auxetic honeycomb sandwich plates. • The proposed ES-MITC3 element combined with HSDT is more accurate than the original MITC3 element. • Influences of geometrical and material properties on the free vibration of auxetic honeycomb sandwich plates are investigated. • An artificial neural network is established to predict the natural frequency of auxetic honeycomb sandwich plates accurately. • The proposed method can be developed to become the FEM benchmark solutions for auxetic honeycomb sandwich plates. [ABSTRACT FROM AUTHOR]

Aiming at achieving excellent energy absorption capacity, a novel periodic auxetic reentrant honeycomb structure is proposed by defining an octagon honeycomb unit cell with various shape parameters and reentrant angles. Additive manufacturing is applied to fabricate three groups of resin samples with different design parameters. Quasi-static compression experimental test is conducted obtaining the effects of negative Poisson's ratio (NPR) on the compressive stress–strain relationship of the proposed structure. The results show the excellent lateral material shrinkage under axial compression and distinct hardening process with sharp stiffness increase when the structure experiences densification. The experiment results are then used to validate the corresponding 3D finite element models. Good agreements are found between the experiment and finite element simulation results. Furthermore, a geometry parameter study is used to analyze the effect of design parameters on energy absorption capacity of the structure and the results can be a good reference for future optimal design of similar meta -materials. To summarize, in addition to the good energy absorption capacity, thanks to the obvious NPR effects and lateral shrinkage behavior, the newly proposed honeycomb meta-material with specific auxetic reentrant design becomes a solid material with low porosity and high stiffness after full compression to provide further protection or support for its neighbor objectives. [ABSTRACT FROM AUTHOR]