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Buckling is one type of unstable structural response which has been known for centuries. Although buckling is generally regarded as a type of undesirable phenomenon, many investigations reported that it can be utilized to generate buckling‐induced metamaterials and structures with negative Poisson's ratio. Recent studies demonstrate that buckling‐induced auxetic behavior will disappear when the base material is changed from elastomer to metal. A pattern scale factor (PSF) method to recover auxeticity of metallic metamaterials and structures was mentioned in previous studies, but the method has not been specifically introduced. Herein, a more detailed introduction of the PSF method is made and some successful case studies are presented. [ABSTRACT FROM AUTHOR]

Auxetic materials exhibit interesting deformation characteristics and excellent mechanical properties. A novel combined tubular structure with tunable stiffness is proposed in this work, aiming to improve the bearing capacity and stability by length design of the central column. Specimens were fabricated via 3D printing technique. Experimental test was performed to study their mechanical property and deformation characteristics under uniaxial compression. The validity of the finite element model was proved by comparing the experimental result with simulation prediction. The compression process and stress-strain curve of the tubular structure with tunable stiffness exhibited four distinct stages (elastic, stiffness change, densification and buckling). Subsequently, a parametrical analysis was conducted to investigate the influences of the central connecting column on the stress-strain response, Poisson's ratio and stability of the structure. By properly choosing the length of the central connecting column, the tubular structure could possess tunable stiffness, higher stability and compressive capacity. Furthermore, this design concept could be of benefit to the development of adaptive structures, smart devices and applications for civil engineering and protective engineering. • The auxetic tubular structure exhibits tunable stiffness and improved mechanical properties. • The stiffness could be tuned artificially through the design of central connecting column. • The influences of the connecting column were explored via parametric analysis. • The stiffness change point ε c t and densification point w ε d t ere proposed via geometric derivation. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to study the tensile performance, deformation characteristics, auxeticity and stability of different auxetic tubular structures generated by cutting method and pattern scale factor (PSF) method using validated finite element analysis. Design/methodology/approach: Two types of auxetic tubular structures were designed by a coordinate transformation method and the PSF adjustment method, respectively. ABAQUS/explicit solver was used for the large deformation analysis and the displacement of key nodes was extracted to calculate Poisson's ratio value and evaluate the deformation of tubular structures. Findings: The random cut method was not suitable for designing auxetic tubular structures. Vertical and horizontal cut approach was suitable, but the change of the tubular diameter was lower than the tubular structures generated by the PSF adjustment method. Research limitations/implications: Simple ways to generate auxetic tubular structure, which can be made into intelligent and foldable equipment, such as annuloplasty rings, angioplasty stents and oesophageal stents. By combined with shape memory polymer, various smart tubular materials and structures with various functions can be designed, especially in medical scaffold and other medical equipment fields. Originality/value: The auxetic characteristic of tubular structure designed by using random cut method has been investigated for the first time. The outcome of this study would be very useful design tubular structures with better mechanical properties. [ABSTRACT FROM AUTHOR]

Novel auxetic tubes (NAT) were designed, fabricated and examined. Their mechanical properties were compared with the original auxetic tube (OAT) by the finite element method and experiments. The results show that NAT increases the specific energy absorption (SEA) without sacrificing the auxetic characteristic. Then, the effect of unit cell parameters on the mechanical properties of NAT tubes was explored. The results show that, in a certain range, rib reduction can improve the SEA of NAT without sacrificing the auxetic effect. To further improve the mechanical properties of NAT, three novel ribbed auxetic tubes (NRAT) were proposed and compared with NAT. It is concluded that the SEA of NAT can be improved by adding a straight rib to the inner long axis of the ellipse. In addition, the effect of straight rib width on the mechanical properties of NRAT was investigated. The results show that the larger the straight rib is, the higher the energy absorption is. Finally, the stability of the 3D auxetic tubular metamaterial is greater than that of the 2D auxetic thin-plate metamaterial by investigating. Due to their desirable mechanical properties, the NAT and NRAT have great potential for applications in medical engineering, vehicle crashworthiness and protective infrastructure. [ABSTRACT FROM AUTHOR]

• A novel perforated negative Poisson's ratio core buckling-restrained brace (NP-BRB) was designed and manufactured. • Seismic performance of the proposed buckling-restrained brace (BRB) was investigated. • The proposed BRB with auxetic core has a desirable seismic property under cyclic loading. • These findings have values in guiding the investigation and design of other metallic dampers regarding auxetics. Auxetic materials could exhibit desirable mechanical properties, e.g., fracture resistance, shear resistance and energy dissipation due to their unique deformation characteristics. However, the seismic performance of auxetics in disaster prevention and mitigation of building structures is rarely studied. In this study, a novel perforated negative Poisson's ratio core buckling-restrained brace (NP-BRB) was designed and manufactured for exploring the hysteretic performance of auxetic metamaterials under cyclic load. Experiments and verified numerical simulations were conducted to investigate the effects of porosity and section weakening rate on the seismic performance. The results show that the NP-BRB has stable hysteretic curves and low compression strength adjustment factor. In addition, the parametric analysis indicated that the energy dissipation capacity of NP-BRB with relatively large section weakening rate could be improved due to auxetic behavior when the average strain exceeds 1%. These findings are beneficial to the applications of auxetic metamaterials in damping devices for mitigating seismic effects. [ABSTRACT FROM AUTHOR]

Auxetic materials and structures have attracted increasing attention because of their extraordinary mechanical properties. Various types of auxetic tubular structures have been designed and studied in diverse fields, including mechanical and medical engineering. In this paper, design methods and advanced manufacturing technologies of auxetic tubular structures are extensively reviewed, including various types of cellular auxetic tubes, nonporous and porous auxetic tubes, macro and micro auxetic tubes. Furthermore, auxetic behaviour, mechanical properties and potential applications of auxetic tubular structures are elaborated. Finally, the challenges and opportunities on the auxetic tubes are discussed to inspire future research work. • Design methods and advanced manufacturing technologies of auxetic tubular structures are extensively reviewed for the first time. • Auxetic behaviour, mechanical properties and potential applications of auxetic tubular structures are introduced. • Challenges and opportunities on the auxetic tubes are discussed to inspire future work. [ABSTRACT FROM AUTHOR]

[Display omitted] • The metamaterial has two very smooth stress plateaus and the plateau stress is not very large. • The metamaterial maintains an obvious auxetic effect under large compressive strains. • Lightweight metamaterials have extremely high specific energy absorption under large strains. • The optimized metamaterial possesses better compressive stability, specific energy absorption and auxetic effect. Auxetic materials and structures have received extensive attention due to their unusual behavior. As one of the structures that can realize the auxetic effect, the elliptic perforated structure has been recently developed, but the previous research on the elliptic perforated is limited to the small deformation stage. At the end of the small deformation stage, the elliptic perforated structure becomes dense and loses the auxetic effect. The available compression stroke is very short and therefore the structure has relatively lower specific energy absorption (SEA). In order to make better use of material, through the buckling of lightweight perforated plates, a newly designed re-entrant elliptical perforated structure is proposed in this work. The re-entrant cells rotate and move inward (the first stage), and finally be compressed by neighbor ones (the second stage). Therefore, the structure undergoes rotational deformation in stage one same as previous perforated plates but specific re-entrant deformation in the second stage, thereby realizing the auxeticity in large deformation. Experimental and numerical results show that the stress–strain curve exhibits double platforms, and the novel structure possesses the auxetic effect throughout the whole compression process. Subsequently, a parametric analysis of the re-entrant distance and the ratio of horizontal and vertical wall thickness was carried out for obtaining greater auxetic effect and better stability of the novel re-entrant elliptic perforated structure. The material utilization rate of the re-entrant elliptic perforated plate was greatly improved, and the application prospect of the re-entrant elliptic perforated was also discussed. [ABSTRACT FROM AUTHOR]

• A novel concrete-filled auxetic stainless steel tube (CFASST) composite structure was proposed. • The proposed CFASST composite structures could provide a desirable radial confinement effect. • Decreasing Poisson's ratio could improve the compressive performance of the CFASST composite structure. Concrete-filled stainless steel tube (CFSST) members take advantage of the high strength and the outstanding corrosion resistance to act as an important role in civil engineering structures. However, the steel tube could not provide the perfect confinement effect for the core concrete during the initial elastic compression stage because Poisson's ratio of the concrete is smaller than that of the stainless steel tube (SST). In this paper, a novel concrete-filled auxetic stainless steel tube (CFASST) composite structure was designed and manufactured to actively restrain the concrete, making the best use of the desirable deformation characteristics of auxetic tubular structures. The axial compressive performance of these CFASST members and their control factors were investigated experimentally and numerically. Test results were discussed in detail which included failure modes, load versus displacement curves and strain analysis. Finally, parametric analyses were conducted to further study the effects of different parameters (Poisson's ratio, thickness of the stainless tube) on the CFSST composite structure under axial compression. It was found that CFASST composite structures possess an unusual deformation mode and an improved confinement effect. [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]

• An acoustic metamaterial plate based on a negative Poisson's ratio structure (NP-AMP) is proposed. • The newly designed structure has a lower frequency bandgap and wider bandwidth compared with traditional structures. • Applying mechanical loading to the NP-AMP enables direct control of the bandgap for shifting to lower frequencies. • The range of bandgap variation is related to the auxetic behavior. Two-dimensional phononic metamaterials, consisting of plates with resonant cylinders, can significantly attenuate waves by opening a subwavelength bandgap, though their characteristic unit cell size is small. To realize the real-time adjustment of the bandgap, external excitations including mechanical load, temperature field, electric field and magnetic field could be introduced, of which applying mechanical load is the most practical way. In this work, an acoustic metamaterial plate based on the negative Poisson's ratio structure (NP-AMP) is proposed and feasible to achieve lower frequency, wider bandgap, and tunable bandgap compared with traditional ones (T-AMP). A counterpart based on the positive Poisson's ratio structure (PP-AMP) is also introduced for comparison. Studies have indicated that the newly designed structure has a lower frequency bandgap and wider bandwidth. With the increase of compression strain, the initial bandgap of PP-AMP gradually moves to a higher-frequency range. In contrast to PP-AMP, the NP-AMP exhibits lower frequency, which is beneficial for the further research of low-frequency bandgap. Moreover, the bandgap variation range can be enlarged by the enhancement of the auxetic behavior. Finally, the variation range of the NP-AMP initial bandgap frequency increased by 62%. The findings in this work will broaden the design of low-frequency broadband acoustic devices used in a dynamic environment, while providing new ideas and methodologies for real-time adjustment of bandgaps. [Display omitted] [ABSTRACT FROM AUTHOR]

• Auxetic metallic metamaterial is designed by variable stiffness factor (VSF) method. • The variable energy factor (VEF) method is proposed. • The accuracies of actual VSF and VEF are discussed under different loading speed. • Layered gradient design can improve mechanical properties of the metamaterials. Auxetic metamaterials have attracted increasing attention due to their exceptional mechanical properties. However, the critical parameters of mechanical response and Poisson's ratio would be changed simultaneously when a geometrical parameter is tuned, which is adverse to achieving the quantitative design of energy absorption by tuning a single geometrical parameter. Thus, the methodology based on tuning densification strain is proposed to design auxetic unit cells with tunable stiffness. In this study, the static performance of 2D metallic auxetic metamaterials designed by the variable stiffness factor (VSF) method is examined experimentally and numerically. To further achieve tunable energy absorption under crushing load, the concept of VSF is extended to variable energy factor (VEF). The dynamic response of verified numerical models is investigated subjected to low-, medium-, and high-velocity crushing. Finally, a functionally graded auxetic structure with different design layers is proposed to effectively solve the issues of high stiffness ratio and initial peak force. These results show that the designed structure has the actual VSF and VEF percentages close to the designed value under low- and medium-velocity crushing. The findings from this study are useful for wider applications of auxetics in protective engineering. [ABSTRACT FROM AUTHOR]

Auxetic foams counter-intuitively expand (shrink) under stretching (compression). These foams can exhibit superior mechanical properties such as resistance to shear and indentation, improved toughness and energy absorption (EA) under several types of loadings. Their unique deformation mechanism and manufacturing process lead to special multiphysics properties such as variable permeability, synclastic curvature and shape memory. Except for traditional energy absorber stuff, the potential applications of auxetic foams have involved biomedicine, aerospace, smart sensing, etc. However, most of the potential applications are restrained in the theoretical stage due to complicated fabrication and a deficiency of stability. For removing the barrier for practical application, a series of issues remain to be resolved, though the explorations of the manufacture methodologies and potential applications are fruitful in the past decades. We present here a review article discussing the state-of-the-art for manufacturing, characterization and applications of auxetic foams. We also provide a view of the existing challenges and possible future research directions, aiming to state the perspective and inspire researchers to further develop the field of auxetic foams. [ABSTRACT FROM AUTHOR]

• A novel auxetic chiral lattice composite is proposed by designing joints of the reinforcement phase. • The mechanical properties and deformation characteristics of four specimens are investigated under uniaxial compression. • The novel auxetic chiral lattice composite exhibits an enhanced stiffness and SEA capacity. • The effects of geometrical parameters and volume fraction of the reinforcement phase on the novel auxetic composites are investigated. Auxetic materials and structures have many potential applications due to their counter-intuitive deformation behavior and desirable mechanical properties. However, auxetic structures have some drawbacks, such as relatively low stiffness and stability. To improve their mechanical performance, one common method is to fill soft materials in auxetic frames, i.e. , auxetic two-phase composites. In this paper, a novel method to further enhance the mechanical properties of auxetic composites has been proposed, which is implemented by designing joints of frames. Mechanical properties and deformation characteristics of these novel composites and their conventional counterparts are investigated experimentally and numerically. The results of finite element analysis and experiments exhibit a good agreement. The energy absorption capacity and auxeticity of the proposed composites could be enhanced by optimizing the design of joints. Subsequently, parametrical studies are conducted to quantify the effects of the geometrical parameters and the volume fraction of the frame. [ABSTRACT FROM AUTHOR]

• A simple methodology for generating auxetic metamaterials with tuneable stiffness is proposed and verified. • The stiffness of the metamaterial could be tuned by using one single parameter of VSF (Variable Stiffness Factor). • The proposed auxetic metamaterials have considerable strength, stability and auxetic behavior. • The potential applications and opportunities of the novel auxetic metamaterial are discussed. Auxetic materials have attracted a considerable attention due to their excellent properties, e.g., fracture resistance, shear resistance, energy dissipation, etc. However, the stiffness of auxetics tends to be much weaker than solid structure because of the existence of internal holes. Inspired by tuning the compacted point of auxetic structures to enhance their stiffness, a systematic methodology for defining a single parametric of variable stiffness scale factor (VSF) to generate auxetic unit cell with variable stiffness has been proposed and verified in this study. Two models with different VSF proportions were investigated experimentally. Different centres of rotation, heights of deformation area, and VSF percentages were analyzed to prove the effectiveness of the method numerically. The results indicate that the compacted strain can be tuned effectively using the designed VSF proportions, and the difference between the designed VSF and real VSF could be reduced by slightly changing the height of deformation area. These desirable characteristics provide a new idea for the optimal design of auxetics, with potential application in protective structures. [ABSTRACT FROM AUTHOR]

• A novel auxetic composite is proposed by filling re-entrant honeycombs with slow recovery foam. • The mechanical properties and auxetic effect of four types of specimens under uniaxial compression are investigated. • The proposed auxetic composite exhibits an enhanced stiffness and a large auxetic effect. • The effects of geometrical parameters and loading rates on the Poisson's ratio and energy absorption capacity are investigated. Auxetic materials have excellent mechanical properties, e.g., indentation resistance, shear resistance, fracture toughness and energy absorption. However, the stiffness of auxetics is normally lower than that of solid structures due to the existence of voids. In this study, to improve the mechanical properties of re-entrant honeycombs, a buffer material called slow recovery foam is filled into re-entrant honeycombs. The mechanical properties and deformation patterns of slow recovery foam-filled re-entrant honeycombs are investigated numerically and experimentally. Parametric studies are conducted to investigate the effects of geometrical parameters on the Poisson's ratio and energy absorption capacity. The results show that filling foam into re-entrant honeycombs will prevent lateral buckling of the structure. Compared with foam-filled hexagonal honeycombs, foam-filled re-entrant honeycombs have higher stiffness. With the increase of the strain rates, the stiffness and energy absorption capacity of slow recovery foam-filled re-entrant honeycombs will increase. With the increase of cell wall thickness and the decrease of cell angle, the energy absorption capacity of slow recovery foam-filled re-entrant honeycombs will also increase. The results indicate that slow recovery foam-filled re-entrant honeycombs are promising in the field of protective engineering. [ABSTRACT FROM AUTHOR]

In this paper, rigid polyurethane (PU) foam was filled into hollow auxetic tube for enhancing the energy absorption. The rigid PU foams and stainless-steel auxetic tube with different geometrical parameters were manufactured, respectively. They were then assembled to form composite foam-filled auxetic tube (FFAT). Four auxetic tubes and four FFATs were respectively tested to examine the enhancement of energy absorption. Tubular types and the effects of parameters including wall thickness, and ellipticity, on FFATs were analyzed numerically by using the validated models. The results show that the overall absorbed energy of FFAT is larger than the sum of single foams and hollow auxetic tube under compression. The geometrical parameters of wall thickness, ellipticity, have a considerable effect on the structural deformation mode and energy absorption. These findings could promote the applications of auxetic composite structures in protective engineering. • The first polyurethane foam-filled auxetic tubes (FFAT) are designed, fabricated and investigated. • The proposed FFATs could exhibit superior mechanical properties under axial compression. • The findings are useful to guide the design of advanced tubular structures for energy absorption. [ABSTRACT FROM AUTHOR]

• A simple seismic metamaterial with ultra-low frequency wide bandgap based on auxetic foam is proposed for the first time. • Band structures, vibration modes and transmission spectrum of the seismic metamaterial are calculated and analyzed. • The influences of geometrical parameters, material parameters value on the bandgap width and location are discussed. Seismic metamaterial (SM) has lately received significant attention in the field of vibration isolation and damping due to its wave manipulation and bandgap properties. However, the limitations of unit cell size and the difference of the material parameters of each component have made it challenging to generate an ultra-low frequency bandgap. In order to overcome this challenge, a novel type of 2D SM composed of auxetic foam and steel is proposed to attenuate seismic waves at ultra-low frequencies. Firstly, the band structure of the SMs and the vibration modes of the upper and lower bounds of the first complete bandgap are calculated and analyzed by using the finite element method, and the mechanism of the bandgap generation is clarified. The transmission spectrum under the Lamb wave incident on the SM is investigated. It is validated that Lamb waves have a good attenuation effect in the frequency range below 10 Hz. Secondly, a parametric study of the SM with auxetic foam-coated hollow steel columns is carried out. The numerical results show that the shape and height of the unit cell, the elastic modulus, density and Poisson's ratio of the auxetic foam play important roles in the formation of the bandgap. Finally, the numerical simulation verifies that adding through holes in the matrix which reduces the equivalent mass density of the matrix could widen the bandgap and enhance the effective attenuation of seismic waves. Based on theoretical model and combined with the exceptional material characteristics of auxetic foam, the focus of the study is to achieve a wide bandgap coverage for the seismic peak spectrum of 2 Hz which causes the principal damage of surface buildings. [ABSTRACT FROM AUTHOR]