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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]

This study proposes to investigate the crushing performance of auxetic honeycombs by combining liquid and solid phase materials in one structure. The multiphase structures were produced by injecting a liquid Gallium metal into the hierarchical voids of the proposed metamaterials and tested at different temperatures (22 and 35 0C), where the melting temperature of Gallium metal is 29.4 0C. The deformation mechanism, compressive strength, absorbed energy, and Poisson's ratio (PR) of the samples was compared at different strains and at different temperatures. Results show that multi-material samples with Gallium metal lead to a progressive deformation mechanism and stabilize the fracture mechanism; however, they only exhibit larger compressive strength in a few cases. In addition, the effects of the phase change of Gallium from solid to liquid when the temperature increase from 22 0C to 35 0C stand out in the percent change of mechanical response. Overall, the presented samples in this work can be recommended to manipulate the collapse mechanism with a multi-material approach of liquid and solid constituents. [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]

• 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 novel auxetic honeycomb (NAH) combined with chiral and re-entrant was proposed. • The EA and SEA of NAH are improved under Quasi-static compression and impact. • Under high-velocity impact, the EA of NAH is better than hexagonal honeycomb. • NAH with thickness gradient shows obvious auxetic behavior under high-velocity impact. Auxetic metamaterials as a cutting-edge field have attracted extensive attention from researchers because of their peculiar deformation mode and excellent mechanical properties. However, the unstable deformation and low stiffness of auxetic structure limit their potential development. To address these limitations, a novel auxetic honeycomb (NAH) has been proposed by combining an original re-entrant hexagonal honeycomb (RH) with cross-chiral honeycomb (CH). The proposed structure has higher stiffness than RH, and more stability than CH. Additionally, the stiffness, densification point, and auxetic behavior can be adjusted by the angle of cell ribs (θ). In this study, the static mechanical properties and deformation behavior of NAH are investigated experimentally and numerically. Furthermore, the energy absorption and deformation behavior of NAH under different impact loadings (low-, medium- and high-velocity) are investigated numerically. Finally, a series of functionally graded NAHs with varying thicknesses are studied to improve the impact resistance of NAH. The results show that NAH has better specific energy absorption than RH and CH under static compression. Moreover, NAH with θ < 90 ° exhibits greater energy absorption capacity compared to NAH with " θ > 90°" at high-velocity impacts. [ABSTRACT FROM AUTHOR]

Lantern, also known as coloured-lantern making, is known for being an ancient traditional craft in China that can be dated back as early as West Han Dynasty. Inspired by the lantern, the lattice element is built by vertically rotating and duplicating the 2D units, then the 3D auxetic metamaterial is formed by connecting the 8 ligaments of the lattice element on two perpendicular planes. As the elastic behaviors associated with this metamaterial are still almost unknown to a large extent, in this study, an analysis has been conducted to investigate how the geometric parameters related to the lattice design influence its elasticity. For this reason, a novel 3D lantern-shaped honeycomb structure (LSH) has been proposed, the Castigliano's second theorem, energy principle, and Moore's theorem are utilized to solve its Young's modulus and Poisson's ratio in the three main directions. The theoretical results exhibit good agreement with the numerical and experimental results. The results showed that the elasticity of LSH structures can be programmed by adjusting a range of geometric parameters. In addition, LSH features a bidirectional zero Poisson effect and a good stress distribution during compression. It shows potential in terms of load-bearing to meet the requirement of lightweight and high stiffness. This structure shows good promise for applications in aerospace, construction and other fields. [ABSTRACT FROM AUTHOR]

Mechanical metamaterials represent a class of deformable systems, which exhibit macroscopic deformations, mechanical, and/or thermal properties. These emerge due to the structure of their subunits rather than their materials composition and typically exhibit anomalous (normally negative) macroscopic structural, mechanical, or thermal property/properties caused by a change in shape/size of the system. Herein, a class of honeycombs is discussed, which push to the extreme the classical definition of "mechanical metamaterials," exhibiting temperature‐tunable Poisson's ratio properties. More specifically, centrosymmetric honeycombs with T‐shaped joints constructed from different materials are shown to exhibit temperature‐dependent Poisson's ratio values, which can be either positive or negative (auxetic) depending on the external stimulus the system is subjected to. The sign and magnitudes of the Poisson's ratio values are explained in terms of particular geometries that these composite honeycomb systems attain at different temperature conditions. In particular, auxeticity is attributed to the transformation of the T‐shaped units to re‐entrant units. Practical aspects on how these properties may be achieved are discussed, including the possibility that the changes in shape, and hence Poisson's ratios, are induced via different extents of dryness on opposite surfaces of ligaments made from absorbent materials. [ABSTRACT FROM AUTHOR]

The nonlinear mechanical responses of tetrachiral honeycombs under large deformation are theoretically analyzed by employing elliptic integrals, and the results are verified by numerical simulations. The nonlinear relationships between normal stress, shear stress, Poisson's ratio and the strain are derived for the tetrachiral honeycombs. It is found that the Poison's ratio of the tetrachiral honeycombs under large deformation is totally different from that under small deformation. The Poisson's ratio can achieve to a large magnitude of 0.8 in the former case, while remains 0 in the latter case. Moreover, the tetrachiral honeycombs exhibit positive Poison's ratio under large tensile-deformation, whilst showing negative Poisson's ratio under large compression-deformation. The magnitude of Poisson's ratio depends on both the honeycomb's deformation and the ligament relative length, while it is insensitive to the ligament thickness. Besides, the coupling effect between tensile (or compression) and shear is observed for the tetrachiral honeycombs. In other words, shear deformation appears within the honeycomb under uniaxial loading. The coupling effect depends on both the honeycomb's deformation and the geometric parameters of the cell structure. And the quantitative relationships among them are derived. This special coupling effect of tetrachiral honeycombs provides a new idea for designing more metamaterials. [ABSTRACT FROM AUTHOR]

Auxetic structures have theoretically superior bending resistance that was previously inaccessible. Compared with the planar two-dimensional (2D) auxetic structures, the three-dimensional (3D) counterparts may exhibit auxetic behavior in multiple directions. Recently, increasing studies have been devoted to studying the mechanical properties of 3D auxetic structures. In this paper, two 3D honeycomb structures were proposed, namely 3D re-entrant honeycomb and 3D hexagonal honeycomb. Subsequently, the mechanical properties, deformation modes, and deformation mechanisms of these two honeycomb structures under three-point bending were investigated experimentally and numerically. Compared with the 3D non-auxetic hexagonal honeycomb, the 3D auxetic re-entrant honeycomb exhibits higher ductility and fracture resistance. In addition, unlike the conventional honeycomb structure, the mid-span section of the 3D auxetic honeycomb exhibits a trapezoidal deformation mode under bending. Finally, the influence of the number of unit cells and geometric parameters on the mechanical properties of the 3D honeycomb structure were systematically studied by parametric analysis. The excellent bending performance provides a basis for the application of auxetic honeycomb in the fields of biomedicine, soft robots, and buffer devices. [Display omitted] • Two 3D honeycomb structures, namely 3D auxetic honeycomb and 3D non-auxetic honeycomb, were designed and fabricated. • The mechanical properties, failure modes, and deformation mechanism of two specimens are investigated under three-point bending. • Compared with the 3D non-auxetic honeycomb, the 3D auxetic honeycomb exhibits better ductility and a trapezoidal deformation pattern at midspan. [ABSTRACT FROM AUTHOR]

• Two different assembled honeycomb structures were designed and studied. • The structures can be transformed by changing the length of connection plates. • The energy absorption capacity of re-entrant honeycomb was investigated. • Re-entrant honeycomb has higher energy absorption than hexagonal honeycomb. Fabricating auxetic metamaterials via an assembling process is a novel and economic method. In this work, an assembled structure that could realize the conversion of positive and negative Poisson's ratio by changing the length of the connection plates was proposed. Two different honeycomb structures of the assembled re-entrant honeycomb (ARH) and assembled hexagonal honeycomb (AHH) were designed, manufactured and studied numerically and experimentally. Dimensions of the two assembled honeycomb structures are consistent. The nominal stress–strain curves of the two assembled honeycombs have similar initial peak stresses, but the assembled re-entrant honeycomb has a higher bearing capacity and shorter stress plateau. Subsequently, the mechanical properties of ARH were studied by changing the three parameters of corrugated plates. Besides, the energy absorption and specific energy absorption of the assembled re-entrant honeycomb were investigated through the numerical method. Finally, the assembled honeycomb structure with the suitable parameter was determined. Tunable mechanical properties of the assembled auxetic structures can be obtained by varying the length of the connection plates. This strategy of assembly can reduce the costs of manufacturing and improve transportation efficiency. The proposed assembled structures are promising in civil and protective engineering. [ABSTRACT FROM AUTHOR]

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

• Optimizing the inclined beams in re-entrant structural elements into buckling beams. • Improved structural element and negative Poisson's ratio metamaterial are designed. • The problem of stress concentration in structural elements is alleviated. • The negative Poisson's ratio characteristic of metamaterial is enhanced. Aiming at the problems of stress concentration and negative Poisson's ratio in the deformation process of the re-entrant structure, a cosine-shaped re-entrant structure negative Poisson's ratio metamaterial is proposed in this paper. By optimizing the inclined beams in the re-entrant structural elements into single cosine, tandem cosine and multiple cosine buckling beams, different configurations of improved re-entrant structural elements are designed. Finite element modeling and quasi-static compression simulations and experiments are carried out for single and periodically arranged re-entrant structures. The results show that the comprehensive stress of the single cosine structure and the tandem cosine structure are reduced by 18.7% and 58%, respectively, and the maximum stress can be reduced by 6.7% and 5.2%, respectively. In addition, the negative Poisson's ratio of metamaterial with a single cosine re-entrant structure is increased by 14% compared with that before the improvement. [ABSTRACT FROM AUTHOR]

Due to their desirable mechanical properties, the MRE honeycomb structures have great potential for applications in civil engineering, vehicle crashworthiness, and protective infrastructure. Moreover, the energy-absorbing performance of the MRE honeycomb structure is substantially improved with the occurrence of the second plateau stress. As shown in article number 2200270 by Xin Ren, Yu Jun Qi, and co-workers, adding two curved ribs to the conventional re-entrant (CRE) honeycomb structure leads to the formation of a modified auxetic re-entrant (MRE) honeycomb structure. [Extracted from the article]

• Hexachiral honeycomb metamaterial with low-frequency vibration isolation and load-bearing capacity is proposed. • The mechanical properties and band gap characteristics are analyzed by both numerical simulation and experiment. • Extreme low frequency band gap (normalized frequency Ω = 0.0043) is obtained. • The influences of structural topology parameters on the mechanical properties and band gap characteristics are discussed. Due to the characteristics of light weight, high specific strength, and excellent damping, auxetic honeycomb structures recently attracted widespread attention. The novel structure with low-frequency vibration isolation and load-bearing capacity became one of the current research hotspots through the improved lattice topology design and associated parameters. For this reason, the authors proposed an auxetic hexachiral acoustic metamaterial with an internal resonant unit. The mechanical properties and band gap (BG) characteristics were analyzed using the finite element method (FEM), and the numerical results were further verified experimentally. Furthermore, the influences of lattice topology parameters on the performance of the above-listed aspects were discussed. Results have shown that the novel metamaterial with extreme low-frequency elastic wave BG and improved mechanical properties can be obtained by combining the hexachiral frame with the internal local resonance unit. [ABSTRACT FROM AUTHOR]

[Display omitted] Natural materials with hierarchical structures usually have superior mechanical properties. Herein, inspired by the macro–micro coupling deformation characteristics of biomaterials, novel hierarchical auxetic-hexagonal honeycombs (AuxHex) metamaterials with various substructures, including equilateral triangles and double arrowheads lattice cells, were constructed. A universal analysis model of the plastic collapse stress was first established, considering the deformation behavior of both the primary and secondary structures. This mechanism-based method gets rid of redundant numerical fitting parameters, and is applicable to different hierarchical lattice structures. Typical hierarchical AuxHex specimens were prepared using selected laser melting and stainless steel. In-plane compression tests and finite element simulation results demonstrated that, in contrast to the regular structures, hierarchical honeycombs exhibit enhancement in their load-bearing capacities and energy absorption ability. The specific modulus of T-AuxHex and A-AuxHex were increased by about 180% and 45%, the specific strength rose by approximately 50% and 15%, and the specific energy absorption was improved by about 160% and 50%. The effects of geometrical parameters were systematically discussed to reveal the mechanisms underlying the enhancement of the above mechanical characteristics. The proposed theoretical model provides a new method for designing the mechanical properties of hierarchical metamaterials by tailoring the type and distribution of secondary structures. [ABSTRACT FROM AUTHOR]

• A simple re-entrant auxetic metamaterial is designed by rotating and connecting 2D re-entrant honeycomb cells. • The energy absorption of the proposed metamaterial is discussed under different design parameters. • The proposed 3D re-entrant auxetic lattice has desirable stiffness and specific energy absorption. • The initial peak stress and energy absorption capacity of the metamaterial can be adjusted via changing design parameters. As a branch of auxetics, the re-entrant hexagonal honeycomb has many superior mechanical performances. However, most research focused on two-dimensional (2D) re-entrant structures or three-dimensional (3D) structures without high compressibility. The energy absorption capacity of such structures is deficient for practical applications. Therefore, it is important to investigate the 3D re-entrant honeycomb structures which can sustain large deformation in order to make the most use of the materials. In this work, a simple 3D re-entrant unit cell is designed, manufactured and examined. The influence of geometric parameters on the deformation mode and energy absorption capacity is investigated numerically. The experimental results are in good agreement with the finite element prediction. The proposed 3D re-entrant auxetic metamaterial not only possesses a greater bearing capacity but also presents a stable compression deformation. The structure exhibits a desirable energy absorption behavior, including obvious auxetic behavior and a long stress plateau. By adjusting the geometrical parameters of the structure, the performances of energy absorption and compression stiffness can be improved. These findings provide a new idea to design 3D auxetic metamaterials and promote their utilization in protective structures. [Display omitted] [ABSTRACT FROM AUTHOR]

Auxetic metamaterials have generated a great deal of interest in recent years. In this letter, a novel approach which can be used to produce such auxetic metamaterials is presented. This method involves the introduction of patterned slit perforations within a sheet/block of material in order to create systems which resemble a large variety of auxetic systems ranging from rotating units to chiral honeycombs. These perforated systems have also been shown to have the potential to exhibit giant negative Poisson's ratios. (© 2015 WILEY-VCH Verlag GmbH &Co. KGaA, Weinheim) [ABSTRACT FROM AUTHOR]