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Pelvic organ prolapse (POP) meshes are exposed to predominately tensile loading conditions in vivo that can lead to pore collapse by 70–90%, decreasing overall porosity and providing a plausible mechanism for the contraction/shrinkage of mesh observed following implantation. To prevent pore collapse, we proposed to design synthetic meshes with a macrostructure that results in auxetic behavior, the pores expand laterally, instead of contracting when loaded. Such behavior can be achieved with a range of auxetic structures/geometries. This study utilized finite element analysis (FEA) to assess the behavior of mesh models with eight auxetic pore geometries subjected to uniaxial loading to evaluate their potential to allow for pore expansion while simultaneously providing resistance to tensile loading. Overall, substituting auxetic geometries for standard pore geometries yielded more pore expansion, but often at the expense of increased model elongation, with two of the eight auxetics not able to maintain pore expansion at higher levels of tension. Meshes with stable pore geometries that remain open with loading will afford the ingrowth of host tissue into the pores and improved integration of the mesh. Given the demonstrated ability of auxetic geometries to allow for pore size maintenance (and pore expansion), auxetically designed meshes have the potential to significantly impact surgical outcomes and decrease the likelihood of major mesh-related complications.

As a kind of common lightweight porous materials, honeycombs have a wide range of applications in aerospace, architecture, packaging and other fields. In this paper, four types of new gradient honeycombs with negative Poisson's ratio are obtained, including angle gradient, thickness gradient and functional gradient, which are obtained by changing the geometric or physical parameters of cells. The dynamic responses of gradient auxetic honeycombs under different impact speeds are studied by ABAQUS display dynamic finite element method, and the deformation profiles of gradient honeycomb models are obtained. The nominal stress–strain curves and energy absorptions of the gradient auxetic honeycombs are studied, and the dynamic bearing capacity of the four kinds of gradient auxetic honeycombs is further analyzed. The results obtained in this paper show that the thickness of cell walls has a great influence on the impact resistance and vibration energy absorption of honeycomb structures. As for gradient honeycombs, the angle gradient honeycomb is better than the other three types in energy absorption, and the functional gradient honeycomb containing ceramic is less deformed. The research results in this paper will provide theoretical guidance for energy absorption, vibration reduction design and applications of honeycomb structures in the engineering field.

In this paper, a work to improve to the auxetic re-entrant cell is reported. This work aims to conserve the negative or zero Poisson's ratio feature of the classical re-entrant cell with no degradation while amplifying the in-plane elastic moduli. To develop and control the stiffness of the cell a new cell was created using a circular wall element in the middle of the classical re-entrant cell. The analytical expressions of the new re-entrant cell were derived and validated by finite element models. Derived analytical expressions of this work can be used to model the classical cell. Using this feature, validation of analytical and numerical models of this work is also provided with a classical cell's experimental works reported in the literature. In the linear region, both the analytical and the finite element models match very closely with the literature experiments. Because of the highly non-linearity of the re-entrant structures, after the linear examination, this work was expanded to model the non-linear behaviour of both the classical and new cells numerically. Literature experiments also verify the non-linear finite element models of this work in means of the classical re-entrant cell's results. Detailed design graphs are given for tuning the rigidity and negative Poisson’s ratios. The presented new design in this paper grants an extra rigidity while providing the same negative Poisson's ratios with those of the classical cells.

This paper develops an auxetic cantilever beam energy harvester (ACBEH) to enhance the harvesting power from ambient vibration sources. A finite element analysis was performed to verify the power increase mechanism of the ACBEH. The simulation model of the ACBEH comprises of three main components: support, tip mass, and cantilever beam with a re-entrant hexagonal auxetic structure in which a piezoelectric element bonded to top of the auxetic region by using a thin elastic layer of epoxy. The performance of the ACBEH was computationally investigated and compared with an equivalent conventional energy harvester with a plain cantilever beam where they are attached to a bridge stay cable. The simulation result shows that the ACBEH excited by a harmonic acceleration of 1 m/s2 at 3 Hz is able to produce electric power of 427.22 μW, which is 2.51 times that of the power produced by the equivalent plain cantilever beam energy harvester (170.17 μW). This paper opens up a great potential of using auxetic cantilever beam applications for different energy harvesting systems in Metamaterials, Acoustics, Civil, Electrical, Aerospace, Biomedical, and Mechanical Engineering.

In nature, the wings shape of a bird can be adjusted to be suitable for all flight situations providing optimal aerodynamic performance. Unfortunately, wings of traditional aircraft are optimized for only a few conditions, not for the entire flight envelope. Therefore, it is necessary to develop the morphing airfoil with smart structures for the next-generation excellent aircraft. Combined with the actuators, sensors and controller techniques, the smart airfoil will bring a revolution for aircraft. Hence, the design of smart structure which is applicable for the morphing airfoil is the first step, especially the flexible airfoil which exhibits many more changeable degrees than rigid structures. In this paper, the composite structure based on re-entrant quadrangular is designed to be applied in the deformable aircraft. The re-entrance structure can show negative Poisson’s ratio performance, also called auxetic, which can offer a great advantage in morphing mechanism. Based on fundamental work about re-entrant quadrangular lattices, the scheme of morphing airfoil is firstly given. Firstly, as shown in the FFT-based homogenization analysis, the enhanced re-entrant lattice outperforms remarkably the original one in stiffness and has similar flexibility. The mechanical characteristics of morphing airfoil with auxetic lattice core are the focus of our paper, which are investigated by using the finite element model. The design loads are extracted from the aerodynamic loads, which are converted to effective nodal loads distributed in the airfoils. The estimated natural model frequencies are given using the model analysis method, which accords with the limits. Furthermore, the compliance performances of the airfoil are investigated under passive and active morphing, respectively. The morphing airfoil with auxetic lattices has the advantages of high deformable, ease of control, variable stiffness, and the ability to bear large amounts of stress. These works offer researchers and designers novel ideas for designing morphing aircraft.

This paper is focused on the identification of the in-plane shear moduli of a new design of auxetic (negative Poisson's ratio) honeycomb configuration with curved cell walls by using analytical and numerical homogenization techniques. The sensitivity of the shear moduli is determined against the various cell geometry parameters. Good agreement between the analytical and numerical simulations is observed. We show that the specific curved wall honeycomb configuration applicated in plates witch build the structure of the wind turbines proposed in this paper possesses a high flexibly compared to the classical hexagonal cell, This leads to the needs of the wind turbine industry to minimize the weight of the wings and also to have a significant flexibility against the wind and the other external dynamic solicitations.

Different from conventional materials, materials with negative Poisson's ratios expand laterally when stretched longitudinally. Known as ‘auxetic’ materials, the effect means they possess particularly fascinating properties, which have recently attracted considerable attention in the literature. A range of auxetic materials has been discovered, theoretically designed and fabricated. Developments in additive manufacturing (AM) techniques enable fabrication of materials with intricate cellular architectures. This paper outlines recent progress in the development of auxetic materials and structures, and their mechanical properties under quasi-static and dynamic loading are analysed and summarised. Limited experimental studies on 3D printed auxetic materials and structures are given more attention, ahead of extensively finite element (FE) simulations. A special focus is dedicated to their large, plastic deformation behaviour and energy absorption performance, which should be stressed in their engineering applications; no review paper has yet been found regarding this. Finally, this paper provides an overview of current study limitations, and some future research is envisaged in terms of auxetic materials and structures, nano-auxetics and additive manufacturing.

In this paper, not only the effect of cell-wall thickness on the deformation mode of metallic auxetic reentrant honeycomb was firstly studied, but also the negative Poisson's ratio (NPR) effect on the crushing stress was also clarified by the quasi-static compressive experiments. Firstly, two types of typical reentrant hexagonal honeycombs with thin-walled and thick-walled cells were manufactured and compressive tests were carried out to characterize the deformation modes, negative Poisson's ratio distribution and crushing stress. Experiment results showed that the deformation mode of thin-walled honeycomb was quite different from that of thick-walled honeycomb, which has not been found in the existing reported papers. Secondly, a finite element (FE) model of the reentrant honeycomb was established and the FE results were systematically compared with the experimental results. The effects of honeycomb cell's number on the compressive deformation and the crushing stress of the honeycomb were studied. The results showed that once the honeycomb contained more than four cells in both transverse and horizontal directions, both the compressive deformation and the crushing stress were close to the experimental results. Finally, the energy absorption characteristics of reentrant honeycomb during compression were discussed. Keywords: Auxetic honeycomb, Compressive behavior, Deformation mode, Crushing stress

A tubular composite structure that is built of two materials, characterized by different Young moduli, is analysed in this paper. The Young’s modulus of one of these materials can be controlled by external conditions e.g., magnetic or electric field, temperature etc. The geometry of the reinforcement is based on typical auxetic re-entrant honeycomb cellular structure. The influence of this external factor on the behaviour of the stretched tube is analysed in this paper. Also, the possibility of creating a tubular composite structure whose cross-section is either shrinking or expanding, while stretching the tube is presented.

The paper moves from a technological process developed in previous works to produce chiral honeycombs made of thin composite laminates. Such approach is applied in this work to manufacture the morphing ribs for a variable camber wing-box. The specifications for such components are obtained by developing a finite element model of a demonstrator, which is designed taking into account aeroelastic performances, structural, and technological issues. In the first part of the paper, the design of such a demonstrator is presented and the role of composite chiral ribs with auxetic behavior is outlined. Production, testing, and numerical studies of manufacturing trials are performed to assess the technological process applied to small-sized chiral units made of different materials, to investigate their mechanical properties, and to validate a numerical approach for design and analysis. A complete chiral composite rib is then produced and tests are carried out to verify the overall structural response and to validate the numerical approach.

We studied the mechanical response of a recently developed new class of mechanical metamaterials based on the paper art of cutting, kirigami. Specially, the geometrical and structural design of representative cut units, via combined line cut, cut-out, and hierarchy of the structure, was explored for achieving both extreme stretchability and/or compressibility in kirigami metamaterials through experiments, alongside geometrical modeling and finite element simulations. The kirigami design was tested on constituent materials including non-stretchable copy papers and highly stretchable silicone rubber to explore the role of constituent material properties. The cut unit in the shape of solid rectangles with the square shape as a special case was demonstrated for achieving the extreme stretchability via rigid rotation of cut units. We found that compared to the square cut units, the theoretically predicted maximum stretchability via unit rotation in rectangle units (aspect ratio 2:1) increased dramatically from about 41% to 124% for the level 1 cut structure without hierarchy, and from about 62% to 156% for the level 2 hierarchical cut structure, which was validated by both experiments and simulations. To demonstrate the achievement of both extreme stretchability and compressibility, we replaced the solid square cut units with porous squares and re-entrant lattice shapes in silicone rubber based metamaterials. We found that a porous structure can enable an extreme compressibility of as high as 81%.

This paper proposes a finite element method (FEM) for the free vibration analysis of sandwich nanoplates with an auxetic honeycomb core. The proposed method uses a third-order shear deformation theory accounting for both shear deformation and stretching effects without any need for shear correction factors. The size-dependent effect is solved using the nonlocal elasticity theory. The auxetic sandwich nanoplate with negative Poisson’s ratio is applied to achieve ultra-light features and high strength. The obtained numerical results by the proposed method are compared with other published works to demonstrate the accuracy and reliability. Moreover, the influence of the nonlocal factor, geometrics parameters, and material properties (especially the auxetic honeycomb parameters) on the free vibration behavior of sandwich nanoplates is also examined in the numerical examples.

Thermal stress has a negative effect on structural safety in many engineering fields, so it is particularly important to eliminate this negative effect as much as possible. This problem can be solved by designing the microstructure of the materials to make the coefficient of thermal expansion (CTE) close to 0, while negative thermal expansion (NTE) materials can become an important part of zero thermal expansion materials. Negative Poisson's ratio (NPR) materials have been favored by researchers because of their bright application prospects in many fields such as medical treatment and engineering. The research of lightweight mechanical metamaterials with both NTE and NPR effects is of great significance for the development of smart sensors with mechanical and temperature sensitivities, and the realization of multi-functional integration of structure. Inspired by the structure of natrolite, a material which can adjust the CTE and Poisson's ratio (PR) in a large range at the same time is designed in this paper. The analytical formulas of the equivalent CTE, PR and Young's modulus are derived and verified by finite element simulation. Meanwhile, the concept of stiffness index is introduced and analyzed by theoretical and finite element methods. Furthermore, the shear modulus of the material is analyzed by finite element method. The results show that the analytical formulas are valid for the material and the material can not only realize NTE and NPR effects at the same time, but also exhibits high stiffness in the principal axis and other directions. In addition, 3D material extended by the proposed 2D material is proposed and verified by finite element method whose parameter analysis have also been carried out, which can achieve NTE and NPR effects in three directions.

The present paper was conducted to calculate Young's modulus and Negative Poisson's ratio (NPR) of a warp and woof (WAW) 3D auxetic structure in three perpendicular directions using an analytical method under uniaxial loading and considering the elastic–plastic behavior of materials. Due to the periodic pattern of the auxetic structure, a unit cell was chosen as a representative volume element (RVE) and its mechanical properties were assessed by developing analytical formulations in the elastic region. To this end, the principle of virtual work along with the concept of lumped plasticity (plastic hinges) were utilized. For validating the proposed analytical model, the 3D finite element (FE) simulations were used. Fairly good correlations were found between the present analytical results and the results of FE simulations. Subsequently, the effects of parameters, such as the initial re-entrant (IRE) angle, the cell thickness, and the auxetic cell aspect ratio on the mechanical properties were investigated. The obtained results revealed that with the increase in the IRE angle, NPR increases in the vertical direction and decreases in two other horizontal directions; it also increases the cell stiffness in three perpendicular directions. The thickness of cell walls does not alter NPR, yet relatively increases the cell stiffness. Furthermore, it was found that the cell aspect ratio has an important role in the mechanical properties of WAW auxetic structures.

A novel two-dimensional (2D) mechanical metamaterial with highly programmable mechanical response under compressive load is presented in this paper by introducing hierarchical rotating structures, in which flexible structures are used to replace the rigid part in conventional rotating rigid structures. Multi-step deformation pathways and negative Poisson’s ratio were observed in in situ compression experiments and finite element simulations, suggesting that the mechanical behavior of the hierarchical metastructure is highly ordered and can be programmed by constraining angles of the proposed metamaterial. This work offers new insights to create mechanical metamaterial using hierarchical rotating structures for flexible devices and crashworthiness applications.

Much research related to negative Poisson's ratio (NPR), or auxetic, structures is emerging these days. Several types of 3D NPR structure have been proposed and studied, but almost all of them had cuboid shapes, which were not suitable for certain engineering applications. In this paper, a cylindrical NPR structure was developed and researched. It was expected to be utilized in springs, bumpers, dampers and other similar applications. For the purpose of parametric analysis, a method of parametric modeling of cylindrical NPR structures was developed using MATLAB scripts. The scripts can automatically establish finite element models, invoke ABAQUS, read results etc. Subsequently the influences of structural parameters, including number of cells, number of layers and layer heights, on the uniaxial compression behavior of cylinder NPR structures were researched. This led to the conclusion that the stiffness of the cylindrical NPR structure was enhanced on increasing the number of cells and reducing the effective layer height. Moreover, small numbers of layers resulted in a late transition area of the load–displacement curve from low stiffness to high stiffness. Moreover, the middle contraction regions were more apparent with larger numbers of cells, smaller numbers of layers and smaller effective layer heights. The results indicate that the structural parameters had significant effects on the load–displacement curves and deformed shapes of cylindrical NPR structures. This paper is conducive to the further engineering applications of cylindrical NPR structures.

Metamaterials that exhibit negative Poisson’s ratio are termed as auxetic materials. The chiral and achiral honeycombs comprising of an array of cylinders connected by ligaments are one class of auxetic metamaterials. These structures have been investigated for their in-plane linear elastic behavior in the past. In this paper, novel bilayer tetra periodic structures are proposed by combining chiral and/or achiral honeycombs along the out-of-plane direction. Finite element (FE) models are developed for estimation of in-plane linear Elastic modulus and Poisson’s ratio. In the first step, the present FE model is verified with the help of experimental data for single layer tetra-chiral and tetra-achiral structures available in the literature. Subsequently, following identical methodology, the linear elastic constants of bilayer structures are computed. A comparison of bilayer tetra periodic structures with the single-layer tetra chiral/achiral metamaterials is presented. Further, a parametric analysis (for varied geometries) was performed to find a correlation between the geometry and mechanical behavior.

Masonry buildings constructed along busy roads are vulnerable to vehicular impacts resulting in damage to property and harm to occupants. This paper presents two strategies that use either carbon fibre or auxetic composite render for mitigating the adverse effects of such impacts and compares the merits of the two strategies. As masonry is a relatively low strength brittle material, the rendering material should possess high energy absorption characteristics (as in auxetic composite) or high strength (as in carbon fibre composite) properties for impact damage mitigation. Towards this end, finite element models incorporating material and contact nonlinearities and (recently developed) carbon fabric and auxetic fabric composite renders possessing positive and negative Poisson’s ratios respectively are developed and applied. These models are validated using experimental datasets and then applied to masonry walls impacted laterally at velocities ranging from 6 km/h to 100 km/h. Results show that the failure mechanism of masonry walls varies from global to local with the increase in the impact velocity and that the auxetic composite render significantly minimises debonding risks, enhances energy dissipation characteristics, reduces the impact force and the impact damage on the masonry walls, compared to carbon fibre composite render.

The vibration and damping performances of carbon fiber-reinforced polymer (CFRP) three-dimensional double-arrow-head (3D DAH) auxetic metamaterials are investigated in this paper. The negative Poisson’s ratio effects of the CFRP 3D DAH auxetic metamaterials are analytically studied by the energy method. 3D finite element models based on Modal Strain Energy approach are developed to analyze their vibration and damping characteristics. To validate the numerical models in the present study, the CFRP 3D DAH auxetic metamaterials are designed and manufactured. The sine-sweep response tests are conducted to investigate their vibration performances. The influence of different inclined corrugated angles, and fiber orientations on the natural frequencies, loss factors and the nominal Young’s modulus are plotted and discussed using validated numerical models. Meanwhile, the effect of Poisson’s ratio on the nominal Young’s modulus, natural frequencies and loss factors is also revealed explicitly. Furthermore, the comprehensive evaluation parameter that simultaneously characterizes the structural bearing capacity and vibration damping performance is further improved through parameter optimization.

In this paper, making use of the coupled deformation features of reentrant and tetrachiral lattices, innovative 3D chiral metamaterials are designed, in which their mechanical properties and deformation mechanisms are explored in details. Firstly, three types of innovative 3D chiral metamaterials are designed based on geometry topology in the x ¯ y ¯ plane, namely: tetrachiral, anti-tetrachiral and hybrid-tetrachiral, respectively. Secondly, the coupled tension and rotation deformation mechanisms of innovative 3D chiral metamaterials are investigated based on large deformation theories of representative unit cell. The theoretical formulas for extension stress, Poisson’s ratio and rotation angle of the square loop are derived, it is found that wide range of negative Poisson’s ratio can be obtained with the proposed 3D chiral metamaterials. Afterwards, tensile experiments are performed, and good agreements between theoretical, finite element and experimental results are presented, verifying the reliability of the theoretical models. Finally, influences of the geometry parameters on the mechanical behaviors of the proposed 3D auxetic metamaterials are also studied.

Auxetic fabrics have many potential applications in technical textiles. Auxetic 3D warp-knitted spacer fabric can be produced by adoption of some special geometrical configuration. Characterization of the geometrical configurations is of vital significance to understand their auxetic property. In this paper, a typical 3D auxetic warp-knitted spacer fabric was studied by synchrotron radiation x-ray computed tomography (SR-CT). Fiber distribution in the fabric was clearly obtained and different types of yarn were extracted separatively. 3D image reconstructed by synchrotron radiation X-ray computed tomography was consistent with the designed geometrical configuration. Besides, 3D model reconstructed lays the foundation for further numerical analysis by FEA.

This paper reports the tensile and impact deformation behavior of an auxetic warp-knitted fabric by using the finite element method. The geometrical model of the fabric was obtained from experiment...

Previous discussions about perforated auxetic metamaterials primarily focused on the ordered systems with high degree of geometric symmetry. However, it is difficult to manufacture or retain the perfect auxetic systems in practical applications. In this paper, three types of disordered perforated auxetic systems including orientated disordered system, dimensional disordered system and complete-disordered system are explored thoroughly. The perforations of interest are oval holes which are advantageous in ensuring auxeticity, reducing stress level and improving material distribution. The designed disordered systems are fabricated by 3D printing technology and then are tested by the uniaxial tension to reveal their mechanical properties and verify the related finite element models. Thereafter, the evolution of mechanical properties of these disordered systems is investigated numerically for the varied perturbed geometric parameters such as the orientation and dimension of oval hole. The results reveal that the disordered systems still show great robustness in auxetic behavior, although the disorder in orientation and dimension exists. A high degree of symmetry in microstructure is not necessary for designing perforated auxetic systems. This provides a great convenience for the flexible and practicable design and application of perforated auxetic metamaterials.

This paper presents a novel meta-functional auxetic unit (MFAU) cell designed to improve performance and weight ratio for structural bridge bearing applications. Numerical investigations were conducted using three-dimensional finite element models validated by experimental results. The validated models were exposed to compression and buckling actions to identify structural failure modes, with special attention placed on the global behaviours of the meta-functional auxetic (MFA) composite bridge bearing. This bearing uses an unprecedented auxetic sandwich core design consisting of multiple MFAU cells. Numerical predictions of the elastic local critical buckling loads of the MFAU cell were in excellent agreement with both the analytical and experimental results, with an observed discrepancy of less than 1%. These results demonstrate that local buckling failures of MFAU cells can potentially be incurred prior to yielding under compression due to their slenderness ratios. Surprisingly, the designed sandwich core used in the MFA composite bridge bearing model can mimic an auxetic structure with significant crashworthiness, implying that this novel core composite structure can be tailored for structural bridge bearing applications. Parametric studies were thus carried out in order to enrich our insight into the MFA composite elements. These insights, stemming from both experimental and numerical studies, enable a novel design paradigm for MFAU that can significantly enhance the structural performance of MFA composite bridge bearings in practice.

A honeycomb is a kind of excellent lightweight structure and a honeycomb sandwich plate with zero Poisson’s ratio (ZPR) core is used widely in morphing structures. In this paper, a sandwich plate composed of a honeycomb core with zero Poisson’s ratio is analyzed for free vibrations and flutter under supersonic airflows. The equivalent elastic parametric formulas of the honeycomb core for zero Poisson’s ratio are proposed. The models are compared for their natural frequencies by theoretical and finite element methods respectively, which verifies the validity of the equivalent elastic parametric formulas and the model for the honeycomb sandwich plate with zero Poisson’s ratio. The influence of the geometric parameters of the honeycomb plate on the vibration frequencies is obtained. Three kinds of honeycomb cores, namely, regular hexagon, auxetic and hybrid with zero Poisson’s ratio, are compared through natural frequencies of the sandwich plate. It is found that the frequency of the zero Poisson’s ratio honeycomb sandwich plate is the second one when the other parameters are the same. The flutter of the honeycomb plate is analyzed by using the first order piston theory under supersonic flows. The critical flutter velocity of the plate is obtained, and the influence of geometric parameters of the honeycomb plate on the critical flutter velocities is obtained.

This paper presents numerical study of deformation and stresses in seat skeleton elements subject to static and dynamic pressure loads. Elastic skeleton made of polyamide or elastomer is taken as an example of a seat material. Auxetic type of seat structure ensures the reduction of real contact stresses between human body and seat, making it more comfortable than typical. FEM analysis is performed using ABAQUS system. Numerical calculations are carried out to determine the nonlinear stiffness characteristics of seat springs. The study makes possible the selection of material and structural topology fulfilling design constraints and additional recommendations concerning structural flexibility, stability and optimal reduction of contact stresses. This paper presents an application of the problem.

Summarization: A band gap region, or simply a band gap, is a range of frequencies where vibrations of certain frequency ranges are isolated. In the present paper, such ranges are sought through the study of different cases for the shape of the unit cells of a lattice, i.e., of an assembly of classical structural elements, such as beams and plates. A lattice with a specific, special designed microstructure is considered in the present investigation. Each particular cell of the examined lattice is studied as a classical composite material consisting of a matrix and the reinforcing core (e.g., matrix-fiber composite), and it is discretized by using two-dimensional plane stress finite elements. The form of the core of the unit cells can be of several shapes, e.g., quadratic, circular, and star. Some of these shapes provide the whole lattice with auxetic behavior, with negative Poisson’s ratio at the homogenized properties. The shape and the microstructure of the lattice is optimized in order to achieve isolation of the desired frequencies. A first attempt on the optimization of star-shaped microstructures is also presented. The optimization is carried out using powerful global optimization methods, such as the genetic algorithms. Results indicate that band gaps may appear in both conventional and auxetic microstructures. Moreover, the appearance and the size of the band gaps depend on the selected microstructure. Παρουσιάστηκε στο: Archive of Applied Mechanics

Re-entrant anti-trichiral honeycomb is a typical auxetic material. The collapse process can be divided into three stages while its negative Poisson's ratio (NPR) effect under large deformation is still unclear. In the present paper, the NPR effects of re-entrant anti-trichiral honeycombs under large deformation are studied by numerical and theoretical method. Numerical results are verified by the experiments with respect to their deformation mechanism and stress-strain behavior. Theoretical formulas are derived to predict the NPR effect of the honeycomb under large deformation. The analytical predictions are in good agreement with the FEM results. It is revealed that the NPR effect of the honeycomb is magnified with the global strain in the second stage while is weaken in the third stage of the deformation process. The decrease of the ligament-ratio and the mean radius will result in more obvious NPR effect. Variation of cell-wall thickness doesn't have much impact on the Poisson's ratio in the second stage, while smaller cell-wall thickness will induce larger NPR in the third stage. The present work is supposed to shed light on the design and fabrication of re-entrant anti-trichiral honeycombs with desired Poisson's ratio.

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.

In recent years, metal additive manufacturing (AM) are widely employed for industrial applications, such as: biomedical, aerospace, automotive, marine and offshore sections. AM demonstrated superior manufacturing efficiencies and economic advantages for advanced lightweight industrial components with unlimited arbitrary topological layouts and complex internal microstructures, and are also employed for fabrication of auxetic materials and structures. In this paper, damage characterizations and mechanical behaviors of selective laser melting (SLM) fabricated 3D re-entrant lattices are investigated based on in-situ interrupted micro-CT test, and simulation based on geometric reconstructed models are performed for exploring the underlying failure mechanisms. Firstly, theoretical models for predicting the mechanical properties of 3D re-entrant lattice are developed, such as stiffness, Poisson's ratio and strength, etc. Secondly, the geometrical errors and fabrication defects of 3D re-entrant lattices are analyzed based on 3D micro-CT scanning, in-situ micro-CT interrupted compression tests are performed for studying the deformation process and failure mechanisms. Finally, image finite element models with the detailed information of the shape, position and distribution of defects of the 3D reentrant lattices are constructed from 3D tomographic images, and numerical simulations are performed for studying the effects of the defects on the mechanical performances of the SLM additive manufactured 3D re-entrant lattice structures. It is shown that the failure behavior of the reentrant lattice is governed not only by its topology, but also by the geometric defects and surface defects. Moreover, the proposed interrupted in-situ micro-CT mechanical loading experiments and image finite element approaches can also shed lights on the relations between fracture failure around the edge and the powder adhesion. The damage evolution process is compared with the numerical simulation results to verify the materials failure modes.

In this paper, the quasi-static compression behavior of graded metallic auxetic reentrant honeycomb was firstly studied. Using the selective laser melting method, the unidirectionally-graded auxetic honeycomb (UGAH) and bidirectionally-graded auxetic honeycomb (BGAH) with the equal mass were fabricated to conduct the compression tests. The deformation mode, crushing stress and Poisson's ratio distribution of graded auxetic honeycombs were presented. Experiment results showed that the compression behavior of graded auxetic honeycomb was different from that of graded honeycomb with positive Poisson's ratio owing to the horizontal shrinkage deformation and the gradient distribution had effects on the crushing stress and Poisson's ratio. Then, a finite element (FE) model of the graded auxetic honeycomb was established and the calculation results were systematically compared with the experimental results. The effects of gradient distribution on the energy dissipation characteristics of the graded auxetic honeycomb were studied. The results showed that the energy dissipation of the UGAH was lower than that of the BGAH before the graded layer with the maximum cell-wall thickness was densified.