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The auxetic structure with negative Poisson's ratio has broad application prospects in many engineering fields. Although it is often simplified as a linear elastic problem in theoretical models, the generally used slender structure, such as the reentrant honeycombs, will inevitably undergo large deformation resulting in significant non-conservative load effects in the service conditions. Therefore, a numerical framework for modeling nonlinear deformation of the auxetic structures under follower loads with the complex variable element-free Galerkin method is developed in this paper. The application of the complex variable meshfree method is to deal with the numerical difficulties caused by mesh distortion that may occur in large deformation problems, and at the same time, it can improve the construction efficiency of meshfree shape functions through the complex variable moving least-squares approximation. The Galerkin weak form of the incremental total Lagrangian formula for large deformation problems with the enforced essential boundary conditions using the penalty method is derived and then discretized in the complex variable meshless implementation. Five numerical examples are presented with detailed convergence study to demonstrate the accuracy of the proposed approach in dealing with non-conservative large deformation of the slender auxetic structures. [ABSTRACT FROM AUTHOR]

Recently, auxetic honeycombs have attracted widespread attention with characteristics of lightweight, excellent energy absorption capacity and high shear stiffness. The present paper proposes the hybrid star-shaped tetra-chiral honeycomb (STCH) by embedding the tetra-chiral honeycomb (TCH) into the star-shaped honeycomb (SSH). The deformation mode and compression behavior of the STCH were studied numerically and compared with that of the SSH and TCH. Particularly, under the impact velocity of 2 m/s, the specific energy absorption (SEA) of the STCH increases by 80 and 179% than that of the SSH and TCH, respectively. Through investigating the effect of impact velocity and relative density on the crushing behavior of the STCH, the deformation modes map was summarized, and the empirical formula of the plateau stress was presented. Subsequently, the detailed parameter analysis of the STCH revealed that in a certain range, the SEA and stability of the STCH increase with the increase of N x , θ , and R , and with the decrease of L 2 and L 1. Finally, the improved STCH (ISTCH) with stable deformation and better crashworthiness was further proposed, and the crashworthiness of it was comprehensively compared with other structures. The result shows the excellent crashworthiness of the ISTCH. Particularly, the SEA of ISTCH can be nearly 8 times higher than that of the TCH. The novel star-shaped tetra-chiral honeycomb (STCH) can absorb more energy due to the increase of plastic hinges and the complex coupling deformation. The deformation modes map of the STCH was summarized and the plateau stress was fitted. The change of radius and cell wall angle can greatly change the Poisson's ratio from positive to negative. The STCH and improved STCH have excellent crashworthiness. [ABSTRACT FROM AUTHOR]

To improve the energy absorption capacity of honeycomb, four novel curved‐ligaments auxetic cellular structures (CLACS‐i [i = 1, 2, 3, 4]) based on the Diabolo‐shaped honeycomb (DSH) are introduced in this article. In the simulation results, it is demonstrated that the energy absorption performance of CLACS‐i (i = 1, 2, 3, 4) surpasses that of DSH under low‐, medium‐, and high‐velocity impacts. However, the negative Poisson's ratio effect of novel structures is inferior to that of DSH. With the increase in impact velocity, the inertial effect of the structure is enhanced, and the deformation mode of the structure changes from global deformation to local deformation. Furthermore, different impact velocities and geometric parameters also affect the energy absorption capacity of the structures. Platform stress and specific energy absorption (SEA) of CLACS‐i (i = 1, 2, 3, 4) increase with the increase of velocity. Under medium‐velocity impact loading, the platform stress and SEA of CLACS‐i (i = 1, 2, 3, 4) increase as the geometric parameter θ decreases and the wall thickness t increases. In this study, a reference is provided for the optimal design and application of honeycomb energy‐absorbing components. [ABSTRACT FROM AUTHOR]

The polygonal honeycomb core has been vertically rotated and spliced to form a new three-dimensional polygonal honeycomb (TPH) structure lattice. Young's modulus and Poisson's ratio for the three main directions of the TPH structure had been derived from Castigliano's second theorem and Moore's theorem. The theoretical results show good agreement with the numerical and experimental results. Meanwhile, the compressive strength of the TPH structure has been analyzed. The results show that the geometric parameters have a significant effect on the elasticity and strength of TPH structures, and the mechanical properties of the TPH structures can be programmed by adjusting the geometric parameters. In addition, the TPH structure exhibits a bidirectional zero Poisson's ratio (ZPR) during compression. This structure shows promise for applications in aerospace, construction, and other fields. This study provides guidance for further research on polygonal honeycomb structures. [ABSTRACT FROM AUTHOR]

A full triangular chiral (Tri-Chi) honeycomb, combining a honeycomb structure with triangular chiral configuration, notably impacts the Poisson's ratio (PR) and stiffness. To assess the random vibration properties of a composite sandwich panel with a Tri-Chi honeycomb core (CSP-TCH), a two-dimensional equivalent Reissner–Mindlin model (2D-ERM) was created using the variational asymptotic method. The precision of the 2D-ERM in free and random vibration analysis was confirmed through numerical simulations employing 3D finite element analysis, encompassing PSD curves and RMS responses. Furthermore, the effects of selecting the model class were quantified through dynamic numerical examples. Modal analysis revealed that the relative error of the first eight natural frequencies predicted by the 2D-ERM consistently remained below 7%, with the modal cloud demonstrating high reliability. The PSD curves and their RMS values closely aligned with 3D finite element results under various boundary conditions, with a maximum error below 5%. Key factors influencing the vibration characteristics included the ligament–rib angle of the core layer and layup modes of the composite facesheets, while the rib-to-ligament thickness ratio and the aspect ratio exert minimal influence. The impact of the ligament–rib angle on the vibration properties primarily stems from the significant shift in the core layer's Poisson's ratio, transitioning from negative to positive. These findings offer a rapid and precise approach for optimizing the vibration design of CSP-TCH. [ABSTRACT FROM AUTHOR]

This study aims to investigate the non-linear free vibration behavior of composite sandwich panels composed of Graphene-reinforced composite (GRC) skins and honeycomb auxetic core. Here, modified Halpin-Tsai micromechanics and bottom-up multi-scale-based schemes are employed to compute the spatial-dependent elastic properties of Graphene nanocomposite and auxetic honeycomb core, respectively. The non-linear kinematic field is based on Kant's higher-order shear-deformation theory and the Green strain. Using the Hamilton principle, the nonlinear governing equations are affirmed and solved further through Picard's iteration-based 2D-isoparametric finite element approximations via Lagrangian elements. The mesh convergence and validation tests are executed to confirm the consistency and correctness of the developed model. The established sandwich model is further employed for various parametric conditions by varying the core-to-face sheet thickness, auxetic honeycomb properties, graphene volume fraction, shell configurations, temperature, and support conditions. These numerous results exemplify the non-linear frequencies at small-to-large amplitudes for the sandwich shell structures and are discussed in detail. In addition, parametric optimization is conducted using the response surface method to investigate the optimal values of auxetic honeycomb parameters, resulting in maximum frequency response. Findings confirm that, within the selected ranges of the geometric parameters of auxetic honeycomb core, higher values of the thickness of the cell rib (∼1.9 cm) and the length of the vertical cell rib (∼0.15 cm) and lower value of the core thickness (∼5 cm) yield the maximum frequency. [ABSTRACT FROM AUTHOR]

AbstractThis article proposes a kind of double concave double-arrow cell. The equivalent thermal expansion coefficient is obtained by using the geometric relation of deformation. The theoretical results agree well with the finite element results. The effect of material matching and geometry size on the equivalent thermal expansion coefficient is discussed. Based on the proposed two-material double-arrow cell, a two-material honeycomb structure is constructed. The thermal expansion coefficient, equivalent elastic modulus and Poisson’s ratio of the structure under thermal load are numerically discussed. It is found that the thermal expansion coefficient of the structure increases with the increase of the thermal expansion coefficient of the material, and the thermal expansion coefficient of the up arrow has a greater effect on the thermal expansion performance of the structure than that of the down arrow. Compared with the single material honeycomb structure, the double-material concave honeycomb structure does not produce the deformation mode of surrounding diffusion, and its longitudinal expansion is smaller. It shows that zero expansion can be achieved by adjusting the material and geometric parameters, and this structure provides a new idea for the design of other zero expansion structures. [ABSTRACT FROM AUTHOR]

In order to obtain a lightweight, high-strength, and customizable cellular structure to meet the needs of modern production and life, the mechanical properties of four thickness gradient honeycomb structures were studied. In this paper, four types of honeycomb structure specimens with the same porosity and different Poisson's ratios were designed and manufactured by using SLA 3D-printing technology, including the honeycomb, square honeycomb, quasi-square honeycomb, and re-entrant honeycomb structures. Based on the plane compression mechanical properties and failure mode analysis of these specimens, the thickness gradient is applied to the honeycomb structure, and four structural forms of the thickness gradient honeycomb structure are formed. The experimental results show that the thickness gradient honeycomb structure exhibits better mechanical properties than the honeycomb structure with a uniform cellular wall thickness. In the studied thickness gradient honeycomb structure, the mechanical properties of the whole structure can be significantly improved by increasing the thickness of cell walls at the upper and lower ends of the structure. The wall thickness, arrangement order, shape, and Poisson's ratio of the cell all have a significant impact on the mechanical properties of the specimens. These results provide an effective basis for the design and application of cellular structures in the future. [ABSTRACT FROM AUTHOR]

Honeycomb structures have attracted wide attention due to outstanding mechanical properties as promising light material structures. Inspired by nature and artistic design, various honeycombs with different microstructural configurations have been designed for the sake of better mechanical performances and functions. Here, the Miura-origami reentrant honeycomb (MRH) structure integrating reentrant honeycombs (RH) and Miura-origami structures is investigated systematically. Dynamic impact behaviors of the present MRH structure are investigated numerically. The deformation modes and energy absorption capacity of RH and MRH are compared under different impact velocities, including low-velocity, medium-velocity and high-velocity. The results show that the plateau stress and the specific energy absorption(SEA) of MRH is much higher than RH. Moreover, the parametric study indicates that raising the inclined angle will decrease the plateau stress and the absolute value of Poisson'ratio for MRH structures. The specific energy absorption curves increase as the inclined angle of MRH grows up. In addition, the MRH with smaller dihedral angle can absorb much more impact energy and the variation of absorbed energy is proportional to the cell wall thickness of the MRH structure. This work is expected to provide a new thought for designing advanced energy absorption metastructures and achieving superior mechanical performances. [ABSTRACT FROM AUTHOR]

As a promising energy absorbing structure, reentrant honeycomb (RH) structures have been focus of interest in recent years. By reasonably adjusting the geometric configuration of the honeycomb cell, advanced structures with unique mechanical properties and deformation behaviors can be designed flexibly and novely. In this work, inspired by the composite laminates, a novel laminated reentrant honeycomb (LRH) structure is developed by controlling the orientations of RH layers for achieving excellent energy absorption capacity. Mechanical and deformation characteristics of the proposed structures under static and dynamic loadings are investigated experimentally and numerically. By comparing with single-layer RH structure with the same thickness, the results demonstrate that LRH structures have better energy absorption capacity. The deformation modes of RH and LRH structures are also discussed and it is noted that the LRH structure with ±30° honeycomb sublayers shows zero Poisson's ratio effect. It is worth emphasizing that LRH with 0° and 90° sublayers presents similar negative Poisson's ratio effect with RH by analyzing the equivalent Poisson's ratio-strain curves. In addition, it is found that the latter structure has the best energy absorption capacity when the thickness of single-layer 0° RH structure equals to 5 mm. This work provides a new and reliable thought to design the advanced protective structures under compression and impact loadings. [ABSTRACT FROM AUTHOR]

Based on a novel multi-arc concave cell, four types of thickness gradient honeycomb structures with positive gradient, negative gradient, symmetric positive gradient, and symmetric negative gradient are constructed by changing cell wall thickness, and the relative density of the structure is deduced. The in-plane impact dynamics of gradient structure are revealed by numerical method. The deformation collapse mode, the dynamic response curve, the energy absorption effect, and the platform stress of different gradient arrangement and impact velocity are analyzed. It is found that gradient arrangement and impact velocity have significant effects on the impact properties of the thickness gradient honeycomb structures. When the impact velocity is low, the structure shows laminar shrinkage deformation, but this phenomenon will gradually disappear with the increase of impact velocity. The results show that the energy absorption capacity of the negative gradient structure is the best under different impact velocities. The platform stress is greatly affected by the impact velocity and less affected by the gradient arrangement. [ABSTRACT FROM AUTHOR]

This paper introduces a new type of flexible rudder surface based on the cosine-type zero Poisson's ratio honeycomb to enhance the adaptive capabilities of aircraft and enable multi-condition, rudderless flight. The zero Poisson's ratio honeycomb structure exhibits exceptional in-plane and out-of-plane deformation capacities, as well as a high load-bearing capability. To investigate the deformation characteristics of flexible rudder surfaces utilizing cosine honeycomb structures, this study undertakes a comprehensive investigation through finite element simulation and 3D printing experiments. Moreover, this study analyzed the impact of honeycomb parameters and layout on the deflection performance and weight. The flexible rudder surface, fabricated from nylon, achieves smooth and consistent chordwise bending deformation, as well as uniform spanwise deformation within a tolerance of ±25°, and the maximum equivalent stress observed was 31.99 MPa, which is within the material's allowable stress limits (50 MPa). Finite element simulation results indicate that once the deflection angle of the rocker exceeds 15°, a discernible deviation arises between the actual deflection angle of the flexible control surface and that of the rocker. Furthermore, this deviation escalates with increasing rocker rotation angles, and this discrepancy can be mitigated by augmenting the number of cosine honeycomb cells within the flexible rudder surface. Finally, a prototype of the flexible rudder surface was successfully produced using 3D printing technology, and the experimental results confirmed the deformation behavior, aligning with simulation outcomes with a deviation of less than 20%. These findings confirm the effective deflection performance of the designed flexible rudder surface, highlighting its potential application in small unmanned aerial vehicles. [ABSTRACT FROM AUTHOR]

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 structures, with re-entrant (inverted hexagonal or bow tie) unit cells, have received considerable interest due to their negative Poisson's ratio property that results in superior mechanical properties. This study proposes a simple method to create non-homogeneous re-entrant honeycombs by modifying the size of chevron crosslinks. The various structural designs were conceived by changing the geometrical dimensions of the crosslinks, namely the length ( l c l ) and the thickness ( t c l ), while maintaining the parameters of the re-entrant cell walls. The influence of the design parameters of chevron crosslinks on the mechanical behaviour of additively manufactured re-entrant honeycombs was investigated experimentally and numerically. The structures were fabricated using the Fused Deposition Modelling (FDM) technique from polylactic acid (PLA) plastic. In-plane quasi-static compression tests were conducted to extract the elastic, plastic, and densification properties of the structures. Furthermore, a Finite Element (FE) model was developed via LS-DYNA R11.0 software, validated experimentally, and was then used to obtain a deeper insight into the deformation behaviour and auxetic performance of various designs. The obtained results revealed that the mechanical performance of re-entrant honeycombs can only be tuned by controlling the geometrical configuration of chevron crosslinks. [ABSTRACT FROM AUTHOR]

Auxetic honeycomb sandwich structures (AHS) composed of a single material generally exhibit comparatively lower energy absorption (EA) and platform stress, as compared to traditional non-auxetic sandwich structures (TNS). To address this limitation, the present study examines the use of aluminum foam (AF) as a filling material in the re-entrant honeycomb sandwich structure (RS). Filling the AHS with AF greatly enhances both the EA and platform stress in comparison to filling the TNS with AF, while the auxetic composite honeycomb sandwich structure effectively addresses interface delamination observed in traditional non-auxetic composite sandwich structures. Subsequently, the positive–negative Poisson's ratio coupling designs are proposed to strengthen the mechanical features of a single honeycomb sandwich structure. The analysis results show that the coupling structure optimizes the mechanical properties by leveraging the high bearing capacity of the hexagonal honeycomb and the great interaction between the re-entrant honeycomb and the filling material. In contrast with traditional non-auxetic sandwich structures, the proposed auxetic composite honeycomb sandwich structures demonstrate superior EA and platform stress performance, suggesting their immense potential for utilization in protective engineering. [ABSTRACT FROM AUTHOR]

Icosahedral B12 serves as a fundamental building block for a variety of boron allotropes and plays a crucial role in enhancing the stability of fullerene-like boron nanoclusters. However, progress in the development of two-dimensional (2D) functional assemblies made from icosahedral B12 has been limited. In this context, we propose a 2D semiconducting boron allotrope (h-B12) using icosahedral B12 as a building block. This structure features a stable honeycomb lattice, with its unit cell comprising two mirror-symmetric icosahedral B12 clusters. The results of first-principles calculations indicate that the band structure exhibits Dirac cones and a relatively high group velocity, similar to graphene. Additionally, it is found to be a material with a negative Poisson's ratio and a relatively low Young's modulus. Finally, our calculations reveal that the zigzag nanoribbon constructed from h-B12 displays prominent edge states at both edges, indicating that this structure represents a potential topological electronic material. Our findings shed light on the design and construction of nano-electronic materials via cluster assembly. [ABSTRACT FROM AUTHOR]

Based on the proposed multi-arc curved edge concave adjustable Poisson's ratio cell, five kinds of sandwich panels with negative Poisson's ratio (NPR) were constructed by changing the in-plane thickness of cells: homogeneous, positive gradient, negative gradient, symmetrical positive gradient, and symmetrical negative gradient. The failure mechanical properties of the sandwich panels under the action of local impact were numerically studied. The influences of impact speed and gradient arrangement modes on the failure mode of the sandwich panels, the punch contact force (PCF) and the energy absorption effect (EAE) were investigated. It is found that the failure behavior of sandwich panels is different under different impact speeds. At the same impact speed, the thickness distribution pattern of the sandwich panel core layer will significantly affect the shock resistance of the panel. The study shows that the EAE of sandwich panels can be effectively enhanced by introducing gradient design method, and the sandwich panels with negative gradient arrangement show the best energy absorption effect. [ABSTRACT FROM AUTHOR]

This study explores the design and performance of axisymmetric hexachiral honeycombs, utilizing the hexachiral honeycomb framework and axisymmetric design method. Four axisymmetric hexachiral honeycombs with distinct arrangements were developed: left–right symmetry hexachiral honeycomb (LSHH), up–down symmetry hexachiral honeycomb (USHH), central symmetry hexachiral honeycomb (CSHH), and subunits symmetry hexachiral honeycomb (SSHH). The deformation patterns and compression behaviors of these honeycombs were comprehensively examined through experimental and numerical simulations, and comparisons were made with a non-symmetric hexachiral honeycomb (NHH). The results indicate that symmetrically designed honeycombs exhibit a larger mean plateau stress than the asymmetrically designed the NHH during low-velocity impacts. The study further discusses deformation patterns, specific energy absorption, and the negative Poisson's ratio effect across the five honeycombs under different parameters. Notably, symmetrically designed honeycombs demonstrate superior specific energy absorption, and the negative Poisson's ratio effect becomes evident at an impact velocity of 10 m/s. However, the advantages of axisymmetric honeycombs diminish at higher impact velocities of 50 m/s and 100 m/s. The Poisson's ratio effects of symmetric honeycombs weaken with an increase in the circular ligament r of the honeycomb. Additionally, the study identifies that platform stress and SEA increase for honeycombs with horizontal cell numbers greater than 6. [ABSTRACT FROM AUTHOR]

A theoretical model has been developed to express the longitudinal and transverse piezoelectric effects in ferro/piezoelectrets. This model is an extension of the classic model based on layer-dielectric structures that focuses on the longitudinal piezoelectric effect. The improved model reveals that the relation between the longitudinal piezoelectric d33 coefficient and the transverse piezoelectric d31 coefficient is associated with Poisson's ratio μ13 (or μ31) and Young's moduli Y1 and Y3. The polarity of the two coefficients is opposite for materials with a positive Poisson's ratio as normally observed in conventional piezoelectric materials, and the same for materials with a negative Poisson's ratio, i.e., auxetic materials. The experimental results available in the literature and obtained from ferroelectret metamaterials with a honeycomb cross-sectional structure and two-dimensional (2D) symmetric structure, called 2D ferroelectret metamaterials, designed and prepared in this study reasonably agree with theoretical predictions. This study not only extends the scope of the metamaterials by inducing the concept of ferroelectret metamaterials but also provides a strategy for designing ferroelectrets with designable properties. [ABSTRACT FROM AUTHOR]

A fatal weakness in flexible electrodes is mechanical fracture of conductive layer that occurs during repetitive stretching and bending deformation. Thereby, suppression of cracks development is crucially important for maintaining the properties of flexible electronics. Herein, topology optimization and structure design methods are utilized to greatly enhance mechanical properties of the existing island-bridge (I-B) structure. The flexible electrodes, with inner-concave honeycomb negative Poisson's ratio (I-CHNPR) structure and I-B structure, are designed and fabricated via screen-printed process, and conductivity is thoroughly investigated. The research demonstrates that the maximum stretching and bending stress of flexible electrodes with I-CHNPR structure-C are decreased by 30% and 28%, respectively, relative to the I-B structure. Fatigue life is enhanced by 18-fold. In addition, flexible electrode has advantages of better self-recovery and excellent conductivity. The flexible electrode proposed in this article is further applicated to realize the collection of ECG signals which has the advantages of wide application, reusable and high accuracy. The as-obtained flexible electrode with the above advantages is expected to greatly contribute to the emerging research field of flexible electronics. [ABSTRACT FROM AUTHOR]

Previous studies used to take the regular configuration as the element of the cellular structures, then carry out geometric optimization on the initial structures. Nowadays, more and more bionic metamaterial have been studied for their unique properties, such as bionic honeycomb tubular nested structure, bionic sinusoidal honeycomb, butterfly honeycomb, bamboo and beetle forewing thin-walled structures. Here, we report a novel gardenia-shaped honeycomb (GSH) by observing the gardenia from nature. Two valuable mechanical properties within GSH were explored in this study, which can simultaneously provide good deformability and zero Poisson's ratio effect. To understand the mechanical properties of GSH, we show by theoretical, numerical, and experimental methods where is a good agreement. The developed theoretical models for calculating the in-plane elastic modulus are based on Euler-Bernoulli beam theorem and energy principle. The numerical and experimental tensile process at coincident strain were captured to strongly show the deformability of GSH. The findings of this study provide essential guidance for the design of GSH structures with the desired mechanical properties. [ABSTRACT FROM AUTHOR]

In this study, the graded hierarchical hexagonal honeycomb (GHHH) integrating gradient design and hierarchical design was fabricated using the 3D-printing technique, and its in-plane elastic properties were investigated theoretically, experimentally, and numerically. Theoretical solutions were developed based on the Euler beam theory to predict the effective elastic modulus and Poisson's ratio of GHHH, and theoretical values were in good agreement with the experimental and numerical results. The effect of gradient design and hierarchical design on the in-plane elastic properties of GHHH was also analyzed and compared. Results showed that the hierarchical design has a more significant effect on Poisson's ratio and adjusting the internal forces of GHHH compared with the gradient design. In addition, it was found that GHHH exhibited higher stiffness compared with regular hexagonal honeycomb (RHH), graded hexagonal honeycomb (GHH), and vertex-based hierarchical hexagonal honeycomb (VHHH) under the constraint of the same relative density, respectively. Specifically, the effective elastic modulus of GHHH can be enhanced by 119.82% compared to that of RHH. This research will help to reveal the effect of integrating hierarchical design and gradient design on the in-plane elastic properties of honeycombs. [ABSTRACT FROM AUTHOR]

Bamboo is an environmentally friendly building structural material. This work investigated the cavity structural characteristics and physical and mechanical properties of honeycomb sandwiches and natural bamboo in the longitudinal direction. The effective elastic parameters of periodically arranged hexagonal bamboo honeycomb cells under in-plane and out-of-plane loads were modeled using analytical and numerical approaches. Then, the effective elastic parameter model of bamboo honeycomb cells was validated by experiments and finite element analysis. The average errors between the calculated and experimental equivalent modulus of elasticity, Poisson's ratio, and shear modulus in the three principal axis directions were 7.43, 4.37, and 8.68%, respectively. The average relativities between the model values of the elastic parameters of the bamboo honeycomb cell and the simulation results in the three directions were 5.46, 5.40, and 6.12%, respectively. The experimental and finite element analysis showed that the constructed effective elastic parameter model of the bamboo honeycomb cell better reflected the state of the bamboo core when subjected to force. This study provides insights for further research on the mechanical properties of bamboo materials and their application in bamboo-based lightweight and high-strength sandwich structures. [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]

This paper presents a novel rhombic star-shaped honeycomb (RSSH) configuration with tunable Poisson's ratio and elastic modulus, and an RSSH with the U-shaped ligaments (URSSH) configuration is generated to analyze the effect of the curved ligaments on the elastic properties of RSSH. Cellular structure of RSSH combines with a rhombic and an improved star-shaped geometry, which can also be subdivided into flexible segments and rigid segments. In-plane elastic properties of the RSSH cell, including Poisson's ratio and elastic modulus, are both derived by analytical model based on flexibility modeling method and Castigliano's second theorem. Based on the guidance of theoretical model, quasi-static tensile experiments and finite element simulation of RSSH and URSSH specimens are carried out with different Poisson's ratio. The experimental results are in good agreement with the theoretical predictions and finite element analysis results. Length of cellular ligaments Lt1, dt have linear relationship with mechanical properties of the RSSH cell under constant angle θ1 and make the cellular configurations with different Poisson's ratio more obtainable. The effect of the symmetry of the flexible segments on the cellular mechanical properties is also analyzed through theoretical prediction. The introduction of asymmetry can bring wider design space of RSSH mechanical properties, especially Poisson's ratio. This work demonstrates the promising potential for applying RSSH configurations in 2D morphing structures with tunable auxetic behaviors. [ABSTRACT FROM AUTHOR]

To realize the one‐dimensional deformation of morphing wings, zero Poisson's ratio (ZPR) honeycomb metamaterials have become a popular research topic due to their lightweight, low in‐plane modulus, and high out‐of‐plane strength. A ZPR honeycomb metamaterial is designed and prepared from short‐cut carbon fiber‐reinforced polyetheretherketone (CF/PEEK) by a 3D printer. The mechanical properties of ZPR honeycomb metamaterials were tested to determine their tensile and bending stiffness. The results show that the metamaterial can achieve 62.3% ± 3.3% in‐plane elastic deformation after optimized structure design. At the same time, metamaterial has a certain bending resistance to keep the airfoil from normal buckling deformation. Moreover, a new test method for evaluating the cycle deformation behavior of flexible morphing wings is proposed. The high‐speed cyclic tension‐compression test showed that H22‐t0.6‐CT has the best stability, which may be related to its lower porosity (2.15% ± 0.12%). These results indicate that ZPR honeycomb metamaterials have great application prospects in the field of morphing wings. Highlights: The printed CF/PEEK wire is treated as a transversely isotropic material.ZPR honeycomb metamaterial allows for more than 50% in‐plane deformation.A new test method to evaluate the cyclic deformation behavior. [ABSTRACT FROM AUTHOR]

In this article, the non‐linear free vibration behavior of sandwich composite panels with sinusoidal corrugations is examined. These panels consist of a top and bottom skin made of a graphene‐reinforced composite, with an auxetic honeycomb core having negative Poisson's ratio. The non‐linear kinematic field is based on Kant's higher‐order shear‐deformation theory and the Green‐strain, which incorporates all the higher‐order terms. By implementing the Hamilton principle, the non‐linear governing equations are affirmed and solved further through 2D‐isoparametric finite element approximations via Lagrangian elements in conjunction with Picard's successive iterative scheme. The comparison and validation tests demonstrate the correctness of the present model. The established sandwich model is further employed for various parametric conditions by varying the core‐to‐face sheet thickness, auxetic honeycomb properties, graphene volume fraction, shell configurations, temperature, and support conditions. These numerous results exemplify the non‐linear frequencies at small‐to‐large amplitudes for the sandwich shell structures and are discussed in detail. In addition, a multi‐objective parametric optimization is conducted using the response surface method to investigate the optimal values of the corrugated auxetic honeycomb shell panel's parameters, resulting maximum frequency. Highlights: Non‐linear vibration of corrugated sandwich shell panel.Graphene reinforced skins and honeycomb auxetic core.Kant's higher‐order shear‐deformation theory and Green‐Lagrange non‐linearity.Hamilton principle and Picard's successive iterative scheme.Multi‐objective parametric optimization and prediction using response surface methodology. [ABSTRACT FROM AUTHOR]

Lattice structures nowadays have gained a peak in research. Inspired by the honeycomb structure and fishbone, this study investigated lattice structures that can provide auxetic behavior and store maximum energy absorption during deformation mode. From that, the study involved designing and producing different modified lattices based on the honeycomb's structure and the fishbone's perspective. The specimens were 3D printed within fused filament fabrication techniques within the additive manufacturing platform of Euromed University of Fes. The conception, production, mechanical testing, and simulation have been employed to get optimum data analysis of the mechanical properties of the designed structures. The results observed under quasi-dynamic compression did not show significant densification behavior; but, the auxetic behavior was seen in all structures, while some suddenly collapsed. The experimental and numerical analysis demonstrated similar deformation behavior and strong agreement in their respective results. Nevertheless, some discrepancies in mechanical values were observed, with a relative percentage error of approximately 1% for both methods. Consequently, owing to the enhanced energy absorption observed in the V2 and V3 structures, it is evident that these modifications hold promise for optimizing the performance of these metamaterials in various practical applications. [ABSTRACT FROM AUTHOR]

This analysis investigated the impact wave response and propagation on a composite sandwich shell when subjected to a low-velocity external shock, considering hygrothermal effects. The sandwich shell was crafted using face layers composed of functional gradient metal–ceramic matrix material and a core layer reinforced with negative Poisson's honeycomb. The honeycomb layer consisted of a combination of viscoelastic polymer material and elastic material. The equivalent parameters for the functional gradient material in the face layers were determined using the Mori–Tanaka and Voigt models, and the parameters for the negative Poisson's ratio honeycomb reinforcement core layer were obtained through Gibson's unit cell model. Parameters relevant to a low-velocity impact were derived using a modified Hertz contact law. The internal deformations, strains, and stress of the composite sandwich shell were described based on the higher-order shear deformation theory. The dynamic equilibrium equations were established using Hamilton's principle, and the Galerkin method along with the Newmark direct integration scheme was employed to calculate the shell's response to impact. The validity of the analysis was confirmed through a comparison with published literature. This investigation showed that a multilayer negative Poisson's ratio viscoelastic polymer material honeycomb-cored structure can dissipate impact wave energy swiftly and suppress shock effectively. [ABSTRACT FROM AUTHOR]

Metamaterials with honeycomb structures have garnered significant attention in energy-harvesting applications. In this study, we present three conventional cantilever resonators with honeycomb substrates featuring positive, zero, and negative Poisson's ratios (PPR, ZPR, and NPR). Polyvinylidene fluoride consisting electrode layers is attached to the substrate surfaces. A process parameter optimization method of honeycomb structure design was proposed, in which finite element simulation for data generation, backpropagation neural network for data prediction, and nondominated sorting genetic algorithm II (NSGA-II) for data optimization. This method aims to determine the optimum geometric parameters of the honeycomb structures, which addresses general cantilever resonators, where the first structural vibration modes are typically of interest and have to match specific target eigenfrequencies for engineering applications. Finite element simulations show that the peak voltage of PPR, ZPR, and NPR resonators at 75 Hz is increased by 12 %, 22 %, and 32 %, respectively, due to optimization. The optimized structures are fabricated and measured to validate the numerical model. The performance of the resonators with cellular materials featuring a full characteristic range of Poisson's ratios is then compared systematically to explore their energy-harvesting potential. The results revealed that the NPR structure exhibits superior performance for energy-harvesting. Moreover, stress distribution and displacement have also been highlighted in this paper. [Display omitted] • A backpropagation neural network is trained to predicting the performance of piezoelectric energy harvester. • An optimization method combining backpropagation neural network and evolutionary algorithm is developed. • The performance of piezoelectric energy harvesters with different cellular substrates are systematically compared. • The optimization results are validated by finite element analysis and experiments. [ABSTRACT FROM AUTHOR]

• A novel composite auxetic reentrant honeycomb structure is designed and fabricated. • The one-stage light gas gun and diffuser-type shock tube were utilized to generate and propagate exponential decaying shock wave. • The effect of gradient form on impact resistance performance was experimentally and numerically investigated. • The effect of relative density of composite reentrant honeycomb structure was analyzed and investigated. The researches on dynamic responses of underwater impulsive loading have been conducted. However, the previous study mainly concentrated on metal sandwich structure and fixed supported boundary. The relative research on composite auxetic re-entrant honeycomb structure and simply supported boundary are rarely. In this paper, the effect of the gradient form and relative density on impact resistance performance of composite auxetic re-entrant honeycomb structure was experimentally and numerically investigated. The one-stage light gas gun was applied to provide initial kinetic energy of the fly plate, and the diffuser-type shock tube was utilized to generate and propagate exponential decaying shock wave. The pressure–time curve was respectively amplified and recorded by the charge amplifier and oscilloscope. The response speed, final deflection of rear panel and failure mode of cores and panels were used to evaluate impact resistance of composite auxetic re-entrant honeycomb structures. Moreover, acoustic-structure interaction algorithm was applied to simulate impact course of specimens in Abaqus/Explicit. The results between experiment and numerical simulation exhibited good consistency. The results indicated that the positive gradient form could excessively slow down response speed of rear panel by dissipating energy of shock wave, and the average gradient demonstrated smaller final displacement of rear panel and less failure compared with graded structures. [ABSTRACT FROM AUTHOR]

Unlike traditional energy dissipation structures that dissipate energy through irreversible plastic deformation or collapse, metamaterials based on friction energy dissipation have attracted attention due to their reusability. This article proposed a novel energy dissipation metamaterial by integrating friction energy dissipation mechanism into negative Poisson's ratio (NPR) structures. The integration of friction energy dissipation mechanism can simultaneously enhance the effective stiffness and NPR effect. The mechanical properties of the proposed structure were investigated using theoretical analysis, experiments, and finite element (FE) simulations. The influence of variables such as internal concave angle, friction coefficient, and number of reinforcing ribs was discussed. The results indicate that both unit cell and honeycomb structure can repeatedly dissipate energy within the elastic range. Compared with the traditional concave hexagonal structure, the effective stiffness and NPR effect were enhanced. This work provides a novel idea for the design of NPR energy dissipation structures. [ABSTRACT FROM AUTHOR]

This study presents a novel three-dimensional orthogonal accordion structure (3D-OAS) with multi-directional zero Poisson's ratios (ZPR) achieved by combining two-dimensional accordion honeycomb structures (2D-AHS) orthogonally. The analysis of its mechanical performance involved deriving equivalent elastic properties using beam theory. Subsequently, a three-dimensional Cauchy equivalent model (3D-CEM) was established using the variational asymptotic method to convert structural orthotropy into material orthotropy. Uniaxial compression tests were conducted on unit-cell and multi-layer 3D-printed specimens to confirm the multi-directional ZPR effects. The in-plane and out-of-plane static behaviors of 3D-OAS panels were evaluated, affirming the accuracy and effectiveness of the equivalent model. Numerical simulations showed that the 3D-CEM required fewer elements and nodes, representing 0.85% and 0.83% of the computing time required by 3D FE model for in-plane and out-of-plane deformation analyses, respectively. The 3D-OAS panel experienced no significant vertical deformation during in-plane tension but exhibited cylindrical deformation with ZPR characteristics under out-of-plane bending. Specifically, normal stresses exceeded shear stresses at the intersection of the two perpendicular horizontal struts. The inclined angle of strut minimally influenced the Poisson's ratio of 3D-OAS but notably impacted the elastic moduli. These findings provide important theoretical support for the design and application of three-dimensional accordion honeycomb structures. • 3D-OAS achieves multi-directional ZPR effects through orthogonal combination. • Mechanical analysis involves deriving equivalent elastic properties. • 3D-CEM transforms structural orthotropy into material orthotropy. • Uniaxial compression tests on unit-cell and multi-layer 3D-printed specimens. • Efficient 3D-CEM with reduced elements and nodes for numerical simulations. [ABSTRACT FROM AUTHOR]

• A novel bi-material multistable auxetic honeycomb (BMAH) with reusable and enhanced energy-absorbing phases was designed. • The crushing stress–strain curve shows three stress plateaus, and BMAH maintains a stable Poisson's ratio even at high strain levels, transitioning from near-zero to negative and then to positive. • Under the selected material combination, the second stress plateau is 8 times greater than the first, and the third stress plateau is 17 times greater than the first, significantly improving energy absorption efficiency. • A theoretical model was established to reveal the deformation mechanism of BMAH and predict the plateau stresses and strain range for each deformation stage. • Effects of geometrical parameters and crushing velocity on BMAH stress plateaus and Poisson's ratio were investigated, and a programmable guide for designing stress plateaus and specific energy absorption is presented. The ideal energy absorption structures, in addition to possessing reusability and high energy absorption efficiency, should also possess multiple desired properties to fulfill various functional applications. In this study, a bi-material multistable auxetic honeycomb (BMAH) is fabricated by using bi-material 3D printing technology. Under in-plane crushing, multiple stress plateaus can be achieved and the Poisson's ratio can be stably tuned, allowing for a transition from near-zero to negative and then to positive. The above characteristics are attributed to the specimen's multi-path deformation. The first stress plateau is only associated with recoverable elastic deformation. The second and third stress plateaus, which are 8 times and 17 times higher respectively than the first, are associated with plastic deformation, significantly enhancing energy absorption efficiency. The deformation mechanism is theoretically analyzed, and the effects of geometric parameters on the performance of BMAH are investigated. In addition, the effect of crushing velocity on the crushing behavior of the BMAH is also discussed. As the crushing velocity increases, the total number of stress plateaus transitions from three initially to two and then to one. The developed BMAH exhibits significant potential applications in multi-stage energy absorbers and smart sensors. [ABSTRACT FROM AUTHOR]

Flexible piezoelectric sensors have received widespread attention in wearable electronics for their ability to convert mechanical energy into electrical energy, while the insufficient output power and complex preparation process have limited their application. In this work, several honeycomb structures based on graphene macro-film (GAMF) were created via laser engraving, which can utilize negative Poisson's ratio (NPR) properties to improve the output electric performance of flexible piezoelectric sensors. The effect of different electrode materials on the piezoelectric output was investigated in the experiments and compared with the theoretical equations, indicating that the output power of the sensor could be enhanced up to 142 % by improving the materials auxetic mechanical properties. The stability tests have proven that the sensors can operate effectively for a long time under different operating conditions. Moreover, the optimized sensor shows powerful potential for monitoring human movements such as finger tapping, joint bending, and foot stepping. This work opens up a new development path for the preparation of convenient and high-performance wearable electronic devices. The negative Poisson's ratio characteristic of the honeycomb graphene macro-film is used to increase the deformation of PVDF film to increase the electrical output performance of the flexible piezoelectric sensor. The optimized sensor can be used to detect human movements. [Display omitted] • Honeycomb graphene macro-films with different mechanical properties were prepared by laser engraving. • Flexible piezoelectric sensors based on honeycomb graphene macro-films are prepared. • The output performance of piezoelectric sensors can be improved by adjusting mechanical properties of electrode materials. • The flexible piezoelectric sensors can be used to detect human movements. [ABSTRACT FROM AUTHOR]

Two-dimensional monolayers are a prime class of materials due to their extensive spectrum of applications. In the present study, the material characteristics of the 1T-Rb 2 Se monolayer are investigated and analysed by employing the first-principles DFT calculations. The computations of structural, electronic, bonding nature, dynamical, optical, thermoelectric, and elastic properties of the theoretically predicted 1T-Rb 2 Se monolayer are effectuated. The 1T-Rb 2 Se monolayer displays a semiconducting nature with the energy gap quantified using various exchange-correlational potentials. The phonon and CPMD was deployed for the conclusions on the dynamical and thermal stabilities. With indirect band gap and good thermal response, the material will have possible applications in photovoltaics and thermoelectrics. Positive Poisson's ratio and elastic tensors validates the elastic strength of the monolayer. The effective masses of charge carriers and its relative ratio are determined from the energy band paraboloids with the deformation potentials for the accuracy of the relaxation time. The 1T-Rb 2 Se is electronically, ionically, dynamically, thermally, and elastically stable that confirms its feasibility for experimental studies. • Rb 2 Se monolayer possess a trigonal honey-comb structure. • Molecular Dynamics (MD) was used to study the thermal stability of the monolayer. • The 2D network of Rb 2 Se monolayer is a semiconductor with an indirect band gap of about 1.59 eV. • The monolayer exhibits good absorption and medium reflectivity in the visible range of the electromagnetic spectrum that makes the monolayer a promising material in photovoltaics and nano-optoelectronics. • The results from the Figure of merit provide material applications in thermo-electric devices. [ABSTRACT FROM AUTHOR]

The presence of serrated ligaments in the re-entrant auxetic honeycomb (abbreviated as serrated RAH) effectively enhances the stiffness while maintaining auxeticity in the re-entrant direction. To investigate its auxetic characteristics, a 3D equivalent Cauchy model (3D-ECM) was established using the variational asymptotic method. The unique aspect is that the engineering constants are obtained by homogenizing the representative unit-cell and then utilized in the 3D-ECM for global analysis. Subsequently, the resulting global responses are fed into the recovery relationships for localized field analysis. The accuracy of the 3D-ECM and the recovered local field distributions were confirmed by comparing them with the results obtained from the three-dimensional FE model (3D-FEM) and the experimental data collected from the 3D-printed specimen. The effects of the geometric parameters on the negative Poisson's ratio and engineering constants were in-depth discussed. Specifically, an optimal value of 0.5 for the re-entrant ratio and d-value (corresponding to the re-entrant angle of 90 degree) yield maximum auxeticity and comparatively higher elastic moduli. In addition, the 3D-ECM greatly enhanced the computational efficiency without compromising the accuracy in predicting global behaviors and local field distributions. The unit-cell tailorability in the proposed model offers valuable guidance for optimizing the design of serrated RAHs. • The presence of serrated ligaments enhance stiffness while maintaining auxeticity. • Engineering constants are obtained by homogenizing the unit-cell within 3D-ECM. • Auxeticity of the serrated RAH is investigated using a VAM-based 3D-ECM. • The accuracy of the 3D-ECM is validated against 3D-FEM and experimental data. • A re-entrant angle of 90-degree yield maximum auxeticity and higher elastic moduli. [ABSTRACT FROM AUTHOR]

• Three kinds of honeycomb structures were printed using carbon fiber reinforced composites, and the tensile mechanical properties of honeycomb structures were studied by combining experimental and simulation analysis methods. Finally, the relationship between fracture toughness and fractal dimension of tensile fracture surface is analyzed by fractal theory. The study employed chopped fiber-reinforced nylon composite, referred to as "Onyx," along with continuous carbon fiber materials. Using the material extrusion manufacturing process, three sandwich structures were created: a conventional, a concave hexagonal with negative Poisson's ratio, and a feather-inspired structure. Tensile testing and finite element simulations were conducted to analyze their tensile properties and crack propagation paths under tension. Fractal dimensions were calculated for each structure: the standard structure had a dimension of 1.4626, the bionic feather-inspired was 1.4810, and the negative Poisson's ratio concave hexagonal structure measured 1.4973. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to evaluate the dynamic behaviour of sandwich toroidal shells composed of a core with negative Poisson ratio (auxetic honeycomb material) and nanocomposite enriched coating layers under impulsive/periodic pressures considering the geometrical nonlinearity. The set of nonlinear equilibrium equations based on the first-order shear deformation theory are and the resultant nonlinear differential motion equations are approximately solved by the Galerkin method and 4th-order Runge–Kutta solution, respectively. The achieved responses show that the amplitude of outward deformations is intensively increased when the proposed sandwich shells are subjected to rectangular periodic and impulsive loadings which shows the destructive effects of this type dynamic loading. The performed parametric studies shows that these destructive effects can be controlled by changing the geometrical properties of the honeycomb cells and the volume fractions of the nanocomposites in the coating layers. It is notable that in the previous studies the nonlinear dynamic response of toroidal shells subjected to various periodic and impulsive pressures was not investigated. However, in the present work, the mentioned dynamic responses were achieved and investigated without spending time-consuming computational. In fact, the novelty of this work is to develop such a robust and efficient tool. [ABSTRACT FROM AUTHOR]

• 3D origami-inspired auxetic honeycomb with omni-directional high stiffness is proposed. • Theoretical models for predicting the elastic mechanical properties of the CFRP composite 3D honeycombs are developed. • The 3D honeycomb can be applied where good load-bearing capacity and obvious auxetic effect are simultaneously desired. • The 3D honeycomb suggests a potential for 3D isotropic auxetic design. Traditional 3D auxetic materials face significant limitations, marked by low stiffness and pronounced anisotropy. To address these challenges, here a new kind of 3D origami-inspired auxetic honeycomb with omni-directional high stiffness is proposed by us. Two simplified theoretical models based on different assumptions are developed to predict structural homogenized elastic properties along the principal axes. Combined theoretical and numerical studies are carried out to reveal the auxetic mechanism and dominated deformation characteristics of the 3D honeycomb. In order to gain a understanding of its elastic anisotropy, directional dependence of structural homogenized Young's moduli, Poisson's ratios and shear moduli are also investigated in detail. A detailed examination of the dependence of structural homogenized Young's moduli, Poisson's ratios, and shear moduli on loading direction is conducted to comprehend its elastic anisotropy. This paper introduces a feasible method for the rapid manufacturing of the 3D honeycomb using high-performance continuous carbon fiber reinforced composite (CFRP) based on hot-pressing molding. Subsequently, the compressive elastic behaviors of CFRP 3D honeycombs are characterized and evaluated through experimental tests. A comparison with traditional 3D auxetic materials reveals the 3D honeycomb's superiority in both multi-axial loading and rapid manufacturing. Additionally, the demonstrative example suggests that the 3D honeycomb can offer nearly isotropic Poisson's ratio of about −0.9. These results not only demonstrate that the 3D honeycomb is an excellent candidate for applications where both good load-bearing capacity and notable auxetic effect are simultaneously desired but also highlight its potential for 3D isotropic auxetic design. [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]

This article investigates the dynamic instability of a stiffened sandwich plate with an auxetic honeycomb core and three-phase hybrid composite (PMMA/GPL/Carbon fiber) layers. To achieve this objective, the governing equations related to the plate and stiffener are expanded using the first-order shear deformation theory (FSDT). The isogeometric analysis (IGA) method is employed to solve these governing equations. The results are compared with data from previously published articles to validate their accuracy and demonstrate the high precision of the isogeometric analysis method for analyzing stiffened sandwich plates. In this study, the dynamic instability of a stiffened sandwich plate is studied by creating a non-conformed interface between the stiffener and the plate surface. Furthermore, this study investigates how stiffeners, geometric and mechanical characteristics of the auxetic honeycomb core, and three-phase hybrid composite layers simultaneously affect the dynamic instability of a sandwich plate. • Dynamic instability of sandwich plates with auxetic honeycomb core and three-phase hybrid composite layers is studied. • The effects of the simultaneous combination of different honeycomb cores and stiffeners are considered. • The effective properties of the nanocomposite-reinforced face sheets were estimated using the Halpin-Tsai law. • Effect of negative Poisson's ratio of auxetic honeycomb core on the dynamic instability of sandwich plate is considered. • The impact of curvilinear stiffener on the dynamic instability of the sandwich plate is studied under various conditions. [ABSTRACT FROM AUTHOR]

• A class of modified hexagonal honeycomb to realize pattern transformation. • Honeycomb's elastic constants are derived by theoretical energy analysis. • Honeycomb structures exhibit auxetic behavior after pattern transformation. • The cell/node of the honeycomb has a rotating behavior after pattern transformation. • The underlying mechanism of pattern transformation is revealed for honeycomb. Pattern transformation, as one of the special properties of mechanical metamaterials, is widely found in elastic porous structures and gradually expanding to honeycomb structures. Inspired by the higher-order flower-like buckling pattern of hexagonal honeycomb, and generalizing the geometry of structures that pattern transformation occurs under uniaxial compression, this paper proposes a Modified Hexagonal Honeycomb(MHH) structure by adjusting the thickness ratio α and the deflection extension angle θ of the cell wall to topologically reconstruct the honeycomb structure to initiate the first-order quasi-flower-like buckling pattern under uniaxial loading. Results show that the quasi-flower-like pattern transformation appears directly for the MHH structure under uniaxial compression, accompanied with a transition of the Poisson's ratio, from positive to negative. And the butterfly pattern, which appears for traditional hexagonal honeycomb only under biaxial loading, is also observed for the MHH under uniaxial compression. The relative size of the nodes among cell walls is believed to play a crucial role on the appearance of the pattern transformation of the honeycomb structure. This work has revealed the underlying physical mechanism for pattern transformation of honeycomb structures, and would also extend the application range of honeycomb structures to the design of elastic dampers, bending/torsion actuators, or robot drive joints. [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]

• 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]

• Size-dependent behaviors of auxetic honeycomb sandwich nanoplates is developed. • The proposed approach utilizes a nonlocal strain-gradient isogeometric analysis which incorporates the effects of both nonlocality and strain gradient. • The sandwich nanoplate consists of a core layer featuring an auxetic honeycomb and two outer skin layers reinforced with graphene nanoplatelets. • The length scale parameters can high-efficiently predict size effects. • Some novel benchmark numerical results are illustrated and introduced. Honeycomb structures, which are known for being lightweight and stiff, are still being researched and developed. They have been used in a wide range of industries, but their full potential has not yet been realized. In this study, a novel computational approach for exploring the size-dependent behaviors of auxetic honeycomb sandwich nanoplates is developed. The proposed approach employs a nonlocal strain-gradient isogeometric analysis integrating the influences of nonlocality and strain gradient into the nanoplate structures. The sandwich nanoplate consists of a core layer featuring an auxetic honeycomb with a negative Poisson's ratio, complemented by two outer skin layers reinforced with graphene nanoplatelets (GNPs). This configuration not only achieves exceptional lightweight characteristics through the utilization of auxetic honeycomb cells but also enhances structural stiffness by incorporating GNPs into the skin layers. The material properties of the core layer are determined using cellular cell formulas, while the reinforcement of the two outer skin layers with GNPs is calculated using the modified Halpin-Tsai model. Numerous numerical examples are conducted to investigate the influence of various parameters on the frequencies of the auxetic honeycomb sandwich nanoplates. Notably, the geometrical dimensions of the auxetic honeycomb cells and the nonlocal and length scale parameters emerge as significant influencers on the results. As the first analysis of honeycomb structures at small dimensions, our findings stand as valuable benchmarks for future analyses. [ABSTRACT FROM AUTHOR]

• A bistable structure was proposed by introducing cosine-shaped beams. • Configuration and geometric parameter can modulate the ν of the structure. • The structural tunable vibration isolation property was verified by experiments and simulations. With the increasing demand for vibration-isolation structures with tunable and multifunctional properties driven by the rapid development of complex engineering applications, metamaterials have emerged as promising candidates for this purpose owing to their extraordinary properties derived from their unique structural configurations. Owing to their unique deformation mechanisms, negative Poisson's ratio structures have been extensively studied in terms of vibration isolation and energy absorption; however, research on their performance tunability remains lacking. This paper describes a bistable honeycomb mechanical metamaterial (BHMM) consisting of cosine-shaped beams, which exhibits transformable Poisson's ratio and tunable vibration isolation properties. The proposed structure exhibited bistable properties, i.e., undergoing a configuration transition under external forces and retaining its existing configuration after the loading was removed. Furthermore, the two stable configurations exhibited distinctive elastic vibration characteristics, allowing the manipulation of elastic wave propagation on a subwavelength scale via local resonant mechanisms. Overall, this study presents a design methodology for multi-performance tunable metamaterials that satisfy the demands of the external environment. For example, the tunable vibration-isolation property of metamaterial makes it intriguing safety protection structures during crash events. [ABSTRACT FROM AUTHOR]

In recent years, origami honeycomb metamaterials have garnered extensive attention from researchers. Re-entrant origami honeycomb metamaterials exhibit excellent mechanical performances by virtue of lightweight, high-energy-absorbing characteristics and diverse configurations. In this study, the gradient re-entrant origami honeycomb metamaterials are designed by changing significant geometric parameters. To investigate the effects of geometric parameters variations on compressive behaviors, the theoretical analysis model of the re-entrant origami honeycomb is built to predict the compression stress under low-velocity and high-velocity impact. Subsequently, the energy absorption of the uniform re-entrant origami honeycomb (UROH), the gradient-thickness re-entrant origami honeycombs (GTROHs) and the gradient-angle re-entrant origami honeycomb (GAROHs)are investigated under different compression velocities. The impact resistances of UROH, GTROHs and GAROHs are discussed systematically. By adjusting the gradient distribution of thickness, the deformation modes and Poisson's ratio curves of the structure could be altered. Furthermore, under the high-velocity impact, the specific energy absorption (SEA) of the unidirectionally negative GTROH is increased by 36% than that of UROH at the strain of 0.29. The SEA of the unidirectionally positive GTROH is higher by 14.4% than that of UROH at the strain of 0.8. In addition, the unidirectionally positive GTROH exhibits better impact resistance performance than UROH by comparing the peak stress and SEA value under different compression velocities. This study is expected to provide the new route for designing advanced origami-inspired honeycomb structures and improving buffer protection devices. • Gradient re-entrant origami honeycombs are proposed by varying significant parameter of cells. • An analytical model is established to estimate the plateau stress of the present structure. • Deformation modes and energy absorption of gradient origami honeycombs are investigated. • The crashworthiness of uniform and gradient re-entrant origami honeycombs are discussed. [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]