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.

A Note on the Effect of Negative Poisson’s Ratio on the Deformation of a Poroelastic Half-Space by Surface Loads

The aim of this note is to study the effect of negative Poisson’s ratio on the quasi-static deformation of a poroelastic half-space with anisotropic permeability and compressible fluid and solid constituents by surface loads. Two particular cases considered are: two-dimensional normal strip loading and axisymmetric normal disc loading. It is found that a negative Poisson’s ratio makes the Mandel-Cryer effect more prominent. It also results in an increase in the magnitude of the surface settlement.

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.

Topology and Shape Optimization of 2-D and 3-D Micro-ArchitecturedThermoelastic Metamaterials Using a Parametric Level Set Method

2-D and 3-D micro-architectured multiphase thermoelastic metamaterials are designed and analyzed using a parametric level set method for topology optimization and the finite element method.An asymptotic homogenization approach is employed to obtain the effective thermoelastic properties of the multiphase metamaterials.Theε-constraint multi-objective optimization method is adopted in the formulation.The coefficient of thermal expansion(CTE)and Poisson’s ratio(PR)are chosen as two objective functions,with the CTE optimized and the PR treated as a constraint.The optimization problems are solved by using the method of moving asymptotes.Effective isotropic and anisotropic CTEs and stiffness constants are obtained for the topologically optimized metamaterials with prescribed values of PR under the constraints of specified effective bulk modulus,volume fractions and material symmetry.Two solid materials along with one additional void phase are involved in each of the 2-D and 3-D optimal design examples.The numerical results reveal that the newly proposed approach can integrate shape and topology optimizations and lead to optimal microstructures with distinct topological boundaries.The current method can topologically optimize metamaterials with a positive,negative or zero CTE and a positive,negative or zero Poisson’s ratio.

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.

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.

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.

Mechanical Response of Honeycomb Structures Under Impact

A honeycomb structure with a negative Poisson’s ratio(NPR)was designed,fabricated,and analyzed for utilization in personal protective clothing(PPC).The mechanical properties were investigated using a quasi-static mechanical testing and the Hopkinson pressure bar experimental system,and results were compared with similar samples containing regular hexagonal and regular quadrilateral honeycomb structures.The experimental results showed that under quasi-static loadings,the concave honeycomb structure had the highest compressive modulus and yield strength,which produced the highest strain absorption energy,anti-deformation performance and energy absorption.When exposed to a dynamic load at a high strain rate,the concave honeycomb also exhibited the highest dynamic compression modulus,the best impact resistance and best energy absorption among the three structures.In summary,the concave honeycomb structure was more resistant to deformation and had higher impact resistance than the regular hexagonal and regular quadrilateral honeycombs,and exhibited better energy absorption,which makes it a good candidate for application as a personal safety protection material.

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.

Using of an Auxetic Structure as Reinforcement of a Bending Reinforced Concrete Beam

Materials which have negative Poisson’s ratio are entitled as auxetics.Auxetics can be designed as micro-to macro-sized structures.The use of auxetics in civil engineering structures has been studied only to a limited extent.In this study,a re-entrant medium-size auxetic structure is employed as reinforcement of a reinforced concrete beam.The beam is subjected to static and dynamic loading conditions and then investigated by means of maximum vertical displacements of the beam.Besides,normal stresses and shear stresses of the concrete are also assessed.To interpret the performance of the auxetic reinforcement,obtained results are compared with the results of another beam which has non-auxetic reinforcement.The results show that these structures behave with bending compatibility as expected and due to the negative Poisson’s ratio,they led to shear strength increase.Auxetic structures can be employed as reinforcement in a beam.Besides,they can be employed without concrete to increase the shear strength in the case of high shear and impact strength if it is needed.

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.

力学超材料的构筑及其超常新功能

力学超材料是具有反直觉力学性质的人工微结构,其性能取决于人工原子的几何结构而不是材料组分。典型的力学超材料通常与4个弹性常数相关联:杨氏模量E,剪切模量G,体模量K和泊松比v。按所调控弹性常数的不同,将几何结构种类繁多的力学超材料分类为负泊松比拉胀材料(v<0,G>>K)、剪切模量消隐五模式反胀材料(G<<K)、负压缩性材料(-4G/3<K<0)、模式转换可调刚度材料(E)、低密度超强仿晶格材料(E/ρ)、负热膨胀材料。基于人工晶格结构和手性/反手性几何结构单元,扼要地论及在人工几何构筑方面的基本情况,以及不同构型与超常力学性能之间的联系。从而为拓展力学超材料的研究领域提供了系统性的架构,展望了面向3D打印技术制备的力学超材料的发展前景。

负泊松比圆弧曲线蜂窝芯结构的力学分析

负泊松比机械超材料独特的力学性能,使其在航空航天、医疗设备、国防工程等领域具有广泛应用前景.文章提出了一种具有负泊松比特性的弧角可变的圆弧曲线蜂窝芯结构,改进了传统内凹六边形蜂窝芯结构的胞元设计.运用能量法给出了不同弧角下圆弧曲线蜂窝芯结构在小形变范围内等效弹性模量和泊松比的理论公式,与有限元结果有较好的吻合度,验证了理论公式的正确性.同时,给出了圆弧曲线弧角,胞元长宽比和杆厚等结构参数对本结构等效弹性模量和泊松比的影响规律.研究结果可为新型负泊松比机械超材料的优化设计及应用提供新的思路.

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.