Topology Optimization of Metamaterial Microstructures for Negative Poisson’s Ratio under Large Deformation Using a Gradient-Free Method

Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.

Model test of negative Poisson’s ratio cable for supporting super-largespan tunnel using excavation compensation method

In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult.Unfortunately,there are few studies on the failure and support mechanism of the surrounding rocks in the excavation of supported tunnel,while most model tests of super-large-span tunnels focus on the failure characteristics of surrounding rocks in tunnel excavation without supports.Based on excavation compensation method(ECM),model tests of a super-large-span tunnel excavation by different anchor cable support methods in the initial support stage were carried out.The results indicate that during excavation of super-large-span tunnel,the stress and displacement of the shallow surrounding rocks decrease,following a step-shape pattern,and the tunnel failure is mainly concentrated on the vault and spandrel areas.Compared with conventional anchor cable supports,the NPR(negative Poisson’s ratio)anchor cable support is more suitable for the initial support stage of the super-large-span tunnels.The tunnel support theory,model test materials,methods,and the results obtained in this study could provide references for study of similar super-large-span tunnels。

Negative Poisson's ratio and peripheral strain of an NPR anchor cable

Materials with a negative Poisson’s ratio effect perform significantly better than traditional materials for rock mass impact resistance,shear resistance,and energy absorption.Based on these advantages,a negative Poisson’s ratio anchor cable(NPR anchor cable)with high elongation and constant resistance was developed and successfully applied in the field of mine disaster control.However,theoretical and experimental research on the negative Poisson’s ratio effect and peripheral strain characteristics of NPR anchor cables is currently incomplete.This study used several theories and methods,such as static tensile,peripheral strain measurement,and static negative Poisson’s ratio measurement,to investigate the radial deformation law of an NPR anchor cable and the negative Poisson’s ratio characteristics.Experimental results elucidated constant resistance changes in an NPR anchor cable during operation,the motion of the constant resistance body in the constant resistance sleeve,and the deformation law of the constant resistance sleeve.Negative Poisson’s ratio characteristics of the NPR anchor cable and its superior energy absorption characteristics were verified and it provided a theoretical and experimental basis for energy absorption mechanisms of an NPR anchor cable.

Energy Absorption by 3D-Printed Mesh Structures with a Negative Poisson’s Ratio

A negative Poisson's ratio(NPR)structure represents optimal impact-resistance with applications in various fields,including the crash box in vehicles,which absorbs impact kinetic energy.The crash box is designed to deform in response to impact,increasing local structural density,which enhances impact resistance performance.Current studies have only focused on the NPR effect in the plane dimension at low-speed loads.Few studies have considered high-speed impact loads on three-dimensional NPR structures.We have developed two types of AlSi10Mg alloy energy-absorbing structures with NPR using three-dimensional printing technology,and have compared our systems with a conventional hexagonal mesh structure.Sample testing involved split-Hopkinson pressure bar measurements,which showed good agreement with dynamic numerical simulations.When subjected to an impact load,the NPR structure exhibited better impact resistance and energy absorption compared with the positive Poisson's ratio structure.The proposed dual-layer hexagonal structure ensures an NPR effect while exhibiting higher strength and improved stability relative to the conventional concave hexagon structure.

Experimental study on the shear performance of quasi-NPR steel bolted rock joints

Quasi-NPR(negative Poisson’s ratio)steel is a new type of super bolt material with high strength,high ductility,and a micro-negative Poisson’s effect.This material overcomes the contrasting characteristics of the high strength and high ductility of steel and it has significant energy-absorbing characteristics,which is of high value in deep rock and soil support engineering.However,research on the shear resistance of quasi-NPR steel has not been carried out.To study the shear performance of quasi-NPR steel bolted rock joints,indoor shear tests of bolted rock joints under different normal stress conditions were carried out.Q235 steel and#45 steel,two representative ordinary bolt steels,were set up as a control group for comparative tests to compare and analyze the shear strength,deformation and instability mode,shear energy absorption characteristics,and bolting contribution of different types of bolts.The results show that the jointed rock masses without bolt reinforcement undergo brittle failure under shear load,while the bolted jointed rock masses show obvious ductile failure characteristics.The shear deformation ca-pacity of quasi-NPR steel is more than 3.5 times that of Q235 steel and#45 steel.No fracture occurs in the quasi-NPR steel during large shear deformation and it can provide stable shear resistance.However,the other two types of control bolts become fractured under the same conditions.Quasi-NPR steel has significant energy-absorbing characteristics under shear load and has obvious advantages in terms of absorbing the energy released by shear deformation of jointed rock masses as compared with ordinary steel.In particular,the shear force plays a major role in resisting the shear deformation of Q235 steel and#45 steel,therefore,fracture failure occurs under small bolt deformation.However,the axial force of quasi-NPR steel can be fully exerted when resisting joint shear deformation;the steel itself does not break when large shear deformation occurs,and the supporting effect of the jointed rock mass is effectively guaranteed.

Support characteristics of flexible negative Poisson’s ratio anchor cable response to blasting impacts

With the gradual decrease and exhaustion of shallow mineral resources,underground mining has progressed to greater depths.Here,the geological environment is significantly more complex and nonlinear,and large deformations of rock masses have great potential to occur.Many geotechnical engineering disasters have occurred even while using Poisson’s ratio(PR)anchor cable supports.To efficiently deal with these issues,a new support material called negative Poisson’s ratio(NPR)anchor cable is proposed;this material can withstand large deformations and provide high constant resistance.In this study,the support characteristics of macro-NPR anchor cable under blasting impact were mainly studied.The support effects of PR anchor cable and macro-NPR anchor cable were compared and analyzed with the help of field experiments and numerical simulations.The results indicate that field experiments and discontinuous deformation analysis accurately reflect the failure state of the selected roadway,as well as the tension and deformation of the anchor cables.The road-way supported by PR anchor cables cannot resist rock bursts under ordinary circumstances.However,the NPR anchor cable-supported roadway resisted a rock burst caused by the impact equivalent to a mine earthquake magnitude above 3;it meets the requirements of roadway stability.

Auxetics in Biomedical Applications: A Review

Materials exhibiting auxetic properties have a negative Poisson’s ratio, which intrigued researchers to understand the behavior of auxetic structure. Several researchers focused on the different auxetic cell designs, while others focused on the auxetic applications. With the advance of additive manufacturing methods, computer-aided design and finite element analysis in recent decades, auxetics have been explored. One of the interesting applications is in the field of biomedical devices or implants, especially for certain natural biomedical organs such as tissues, certain ligaments that have auxetic properties. This paper is an overview of auxetic design approaches and biomedical applications.

Data-Driven Structural Design Optimization for Petal-Shaped Auxetics Using Isogeometric Analysis

Focusing on the structural optimization of auxetic materials using data-driven methods,a back-propagation neural network(BPNN)based design framework is developed for petal-shaped auxetics using isogeometric analysis.Adopting a NURBSbased parametric modelling scheme with a small number of design variables,the highly nonlinear relation between the input geometry variables and the effective material properties is obtained using BPNN-based fitting method,and demonstrated in this work to give high accuracy and efficiency.Such BPNN-based fitting functions also enable an easy analytical sensitivity analysis,in contrast to the generally complex procedures of typical shape and size sensitivity approaches.

Full‑Fiber Auxetic‑Interlaced Yarn Sensor for Sign‑Language Translation Glove Assisted by Artificial Neural Network

Yarn sensors have shown promising application prospects in wearable electronics owing to their shape adaptability, good flexibility, and weavability. However, it is still a critical challenge to develop simultaneously structure stable, fast response, body conformal, mechanical robust yarn sensor using full microfibers in an industrial-scalable manner. Herein, a full-fiber auxetic-interlaced yarn sensor(AIYS) with negative Poisson’s ratio is designed and fabricated using a continuous, mass-producible, structure-programmable, and low-cost spinning technology. Based on the unique microfiber interlaced architecture, AIYS simultaneously achieves a Poisson’s ratio of-1.5, a robust mechanical property(0.6 c N/dtex), and a fast train-resistance responsiveness(0.025 s), which enhances conformality with the human body and quickly transduce human joint bending and/or stretching into electrical signals. Moreover, AIYS shows good flexibility, washability, weavability, and high repeatability. Furtherly, with the AIYS array, an ultrafast full-letter sign-language translation glove is developed using artificial neural network. The sign-language translation glove achieves an accuracy of 99.8% for all letters of the English alphabet within a short time of 0.25 s. Furthermore, owing to excellent full letter-recognition ability, real-time translation of daily dialogues and complex sentences is also demonstrated. The smart glove exhibits a remarkable potential in eliminating the communication barriers between signers and non-signers.

Effect of Axial Deformation on Elastic Properties of Irregular Honeycomb Structure

Irregular honeycomb structures occur abundantly in nature and in man-made products,and are an active area of research.In this paper,according to the optimization of regular honeycomb structures,two types of irregular honeycomb structures with both positive and negative Poisson’s ratios are presented.The elastic properties of irregular honeycombs with varying structure angles were investigated through a combination of material mechanics and structural mechanics methods,in which the axial deformation of the rods was considered.The numerical results show that axial deformation has a significant influence on the elastic properties of irregular honeycomb structures.The elastic properties of the structure can be considered by the enclosed area of the unit structure,the shape of the unit structure,and the elastic properties of the original materials.The elastic properties considering the axial deformation of rods studied in this study can provide a reference for other scholars.

A novel wavy non-uniform ligament chiral stent with J-shaped stress-strain behavior to mimic the native trachea

Tracheal stents are an important form of treatment for benign or malignant central airway obstruction.However,the mechanical behavior of current tracheal stents is significantly different from that of the native trachea,which leads to a variety of serious complications.In this study,inspired by the structure of the native trachea,a wavy non-uniform ligament chiral tracheal stent is proposed,in which J-shaped stress-strain behavior and negative Poisson's ratio response are achieved by replacing the tangential ligament of tetrachiral and anti-tetrachiral hybrid structure with a wavy non-uniform ligament.Through the combination of theoretical analysis,finite element analysis and experimental tests,a wide range of desired J-shaped stress-strain curves are explored to mimic the native porcine trachea by tailoring the stent geometry.Besides,the negative Poisson’s ratio and auxetic diameter curves versus axial strain of the stent are also studied in detail,thus contributing to the enhancement of cross-section ventilation and reducing the migration of the stent.This novel tracheal stent with a unique microstructure shows a potential to perfectly match the physiological activities of the native trachea and thereby reduce potential complications.

Unit Cell Modelling of Auxetic Structure

Auxetic material structures exhibit a negative Poisson ratio. The structure expands in the axial and transverse directions under tensile loading and vice versa under compression loading. Many fabricated designs for auxetic materials exist such as re-entrant hexagonal, chiral, and arrowhead geometries. This paper studies the unit cell of the re-entrant hexagonal geometry to understand how changing the internal angle and fillet radius of the structure affects the Poisson’s ratio. The material chosen for this study is acrylonitrile butadiene styrene (ABS) due to its availability and frequent use in additive manufacturing. The study was based on finite element analysis. It is observed that the direction of load applied to the unit cell affects the unit cell strain, Poisson’s ratio, and maximum load capacity before failure responses. It is noticed that the re-entrant cell starts by showing a standard non-auxetic behavior until it reaches a specific axial strain value. A quadratic correlation is identified between axial and transverse strain. Designing an auxetic structure starts with understanding the behavior of a unit cell structure. The auxetic structure design is a complex process that requires a compromise between auxetic property to be achieved and load capacity via avoiding stress concentration zones.

Impact and explosion resistance of NPR anchor cable:Field test and numerical simulation

With the reduction of shallow resources,the degree of damage and the frequency of dynamic hazards,such as deep rock bursts and impact ground pressure,are increasing dramatically.However,the existing support materials are incapable of meeting the safety require-ments of the refuges and roadways under a strong impact force.To effectively solve these problems,a novel negative Poisson’s ratio(NPR)anchor cable with excellent properties,such as impact resistance and the ability to withstand large deformation,is proposed.In the present study,a series of field tests and numerical simulations are conducted to investigate the mechanical and support charac-teristics of NPR anchor cables under blast impact.Laboratory mechanical tests show that NPR anchor cables can maintain constant resistance and produce large deformation under the action of multiple drop hammer impacts.According to the results of field tests,the roadway supported by conventional anchor cables was unable to endure the blast impact,while the roadway supported by NPR anchor cables was able to withstand the severe impact equivalent to a Class 3 mine earthquake.The dynamic response of the NPR anchor cable that supports the roadway under explosion is investigated using the innovative coupled modeling approach that combines the finite element method and the discrete element method,and the support effect of the NPR anchor cable is verified.The study shows that the NPR anchor cable has a superior impact and blast resistance performance,and a broad application prospect in the support of chambers and roadways that are at high risk of rock bursts and impact ground pressure.

3D-printed auxetic-structured intervertebral disc implant for potential treatment of lumbar herniated disc

In this study,a novel artificial intervertebral disc implant with modified“Bucklicrystal”structure was designed and 3D printed using thermoplastic polyurethane.The new implant has a unique auxetic structure with building blocks joined“face-to-face”.The accompanied negative Poisson’s ratio enables its excellent energy absorption and stability under compression.The deformation and load distribution behavior of the implant under various loading conditions(bending,torsion,extension and flexion)has been thoroughly evaluated through finite element method.Results show that,compared to natural intervertebral disc and conventional 3D implant,our new implant exhibits more effective stress transfer and attenuation under practical loading conditions.The implant’s ability to contract laterally under compression can be potentially used to alleviate the symptoms of lumbar disc herniation.Finally,the biocompatibility of the implant was assessed in vitro and its ability to restore the physiological function of the disc segment was validated in vivo using an animal model.

Design concepts of an aircraft wing： composite and morphing airfoil with auxetic structures

This paper is categorized into two parts. （1） A frame work to design the aircraft wing structure and （2） analysis ofa morphing airfoil with auxetic structure. The developed design frame work in the first part is used to arrive at the sizes of the various components of an aircraft wing structure. The strength based design is adopted, where the design loads are extracted from the aerodynamic loads. The aerodynamic loads acting on a wing structure are converted to equivalent distributed loads, which are further converted point loads to arrive at the shear forces, bending and twisting moments along the wing span. Based on the estimated shear forces, bending and twisting moments, the strength based design is employed to estimate the sizes of various sections of a composite wing structure. A three dimensional numerical model of the composite wing structure has been developed and analyzed for the extreme load conditions. Glass fiber reinforced plastic material is used in the numerical analysis. The estimated natural frequencies are observed to be in the acceptable limits. Furthermore, the discussed design principles in the first part are extended to the design of a morphing airfoil with auxetic structure. The advantages of the morphing airfoil with auxetic structure are （i） larger displacement with limited straining of the components and （ii） unique deformation characteristics, which produce a theoretical in-plane Poisson＇s ratio of -1. Aluminum Alloy AL6061-T651 is considered in the design of all the structural elements. The compliance characteristics of the airfoil are investigated through a numerical model. The numerical results are observed to be in close agreement with the experimental results in the literature.

Programmable soft bending actuators with auxetic metamaterials

Soft robotics has been receiving increasing attention due to its flexibility and adaptability offered by embodied intelligence. A soft robot may undergo complex motions including stretching,contraction,bending,twisting,and their intricate combinations.Among these basic motions,bending plays a central role when a robot accomplishes tasks such as locomotion,grasping and manipulation. Although a rich repertoire of bending mechanisms has been reported,a systematic and rational design framework is still lack. In this paper,we provide a novel design strategy for soft bending actuators which allows integral modeling and design optimization. Nowadays,metamaterials are emerging as a new tool for soft robots,by encoding the desired complex motions directly within the material architectures,leading to conformable monolithic systems. We combine pneumatic actuators and flexible metamaterials to provide an alternative solution to soft bending actuators,with advantages of compact design,large bending motion,and convenient fabrication. A regular pneumatic chamber is embedded inside auxetic and non-auxetic metamaterials,and bending is generated when inflated. We carry out dimensionless analysis to identify the key design variables. To provide insight into design optimization,we develop a computation framework by modeling metamaterial structures with beam elements and the inner chamber with shell elements as an integral part,allowing efficient simulation of the coupled system. We systematically investigate how the bending angle varies with the key design variables and find the optimal design parameters.The experimental results are well in line with the simulation,and a remarkable bending motion of 0.43°/mm is achieved.

开挖补偿法防控深部地下岩爆灾害——引汉济渭工程秦岭输水隧洞案例分析

Rockburst disasters occur frequently during deep underground excavation,yet traditional concepts and methods can hardly meet the requirements for support under high geo-stress conditions.Consequently,rockburst control remains challenging in the engineering field.In this study,the mechanism of excavation-induced rockburst was briefly described,and it was proposed to apply the excavation compensation method(ECM)to rockburst control.Moreover,a field test was carried out on the Qinling Water Conveyance Tunnel.The following beneficial findings were obtained:Excavation leads to changes in the engineering stress state of surrounding rock and results in the generation of excess energy DE,which is the fundamental cause of rockburst.The ECM,which aims to offset the deep excavation effect and lower the risk of rockburst,is an active support strategy based on high pre-stress compensation.The new negative Poisson’s ratio(NPR)bolt developed has the mechanical characteristics of high strength,high toughness,and impact resistance,serving as the material basis for the ECM.The field test results reveal that the ECM and the NPR bolt succeed in controlling rockburst disasters effectively.The research results are expected to provide guidance for rockburst support in deep underground projects such as Sichuan-Xizang Railway.

Wave Propagation Characteristics in Thick Conventional and Auxetic Cellular Plates

Based on Mindlin plate models and Kirchhoff plate models,this study was concerned with the wave propagation characteristics in thick conventional and auxetic cellular structures,with the objective to clarify the effects of negative Poisson＇s ratio,shear factor and orthotropic mechanical properties on the dynamic behaviors of thick plates.Numerical results revealed that the predictions using variable shear factor in Mindlin plate models resulted in high wave frequencies,which were more significant for plates with negative values of Poisson＇s ratio.The present study can be useful for the design of critical applications by varying the values of Poisson＇s ratio.

On the application of additive manufacturing methods for auxetic structures: a review

Auxetic structures are a special class of structural components that exhibit a negative Poisson’s ratio(NPR)because of their constituent materials,internal microstructure,or structural geometry.To realize such structures,specialized manufacturing processes are required to achieve a dimensional accuracy,reduction of material wastage,and a quicker fabrication.Hence,additive manufacturing(AM)techniques play a pivotal role in this context.AM is a layer-wise manufacturing process and builds the structure as per the designed geometry with appreciable precision and accuracy.Hence,it is extremely beneficial to fabricate auxetic structures using AM,which is otherwise a tedious and expensive task.In this study,a detailed discussion of the various AM techniques used in the fabrication of auxetic structures is presented.The advancements and advantages put forward by the AM domain have offered a plethora of opportunities for the fabrication and development of unconventional structures.Therefore,the authors have attempted to provide a meaningful encapsulation and a detailed discussion of the most recent of such advancements pertaining to auxetic structures.The article opens with a brief history of the growth of auxetic materials and later auxetic structures.Subsequently,discussions centering on the different AM techniques employed for the realization of auxetic structures are conducted.The basic principle,advantages,and disadvantages of these processes are discussed to provide an in-depth understanding of the current level of research.Furthermore,the performance of some of the prominent auxetic structures realized through these methods is discussed to compare their benefits and shortcomings.In addition,the influences of geometric and process parameters on such structures are evaluated through a comprehensive review to assess their feasibility for the later-mentioned applications.Finally,valuable insights into the applications,limitations,and prospects of AM for auxetic structures are provided to enable the readers to gauge the vitality of such manufacturing as a production method.

Computational Studies of Porous Head Protection Structures for Human Cranium under Impact Loading

This paper looks into the effects of various porous structures used in the construction of the shell of a protective helmet on the energy absorption capacity and their efficacy in protecting the head/skull against impact force.It is well known that porous structures are very effective for energy absorption;hence,they have been widely used to reduce the negative effects of impact and explosion loads on the human skull.Porous shell structures,made from titanium alloy(Ti–6Al–4V)and,comprised of several periodic topological configurations,namely the more common rectangle and hexagonal honeycomb,as well as those having auxetic properties,namely the concave honeycomb and double-arrow,are studied by means of numerical modeling.The reliability of the numerical model is validated with the published experimental results.For the double-arrow configurations,the study involves three different densities,and the structural energy absorption capacity of the double-arrow shells increases with density.For the same density,the energy absorption capacity of the rectangular shell is the best,and that of the honeycomb is the worst.The superior performance of the rectangular configuration is partly derived from the fact that the orientation of the struts in this structure is aligned along the direction of the impact force.Further comparison of energy absorption capacity is made between the porous shell and a shell having a traditional titanium monolayer.The severe plastic deformation in the solid titanium shell(traditional monolayer shell)is detrimental to the overall effectiveness of head protection gear.Apart from this,compared with the Kevlar composite laminated shell of the same mass,both the solid and porous titanium shells provide considerable protection to the human head.The comprehensive comparisons show that the porous design on the titanium shell is beneficial for mitigating the risks of traumatic brain injuries(TBIs).