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.

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.

Multidisciplinary Design Optimization of Crash Box with Negative Poisson’s Ratio Structure

To improve the crashworthiness and energy absorption performance,a novel crash box negative Poisson’s ratio(NPR)structure is proposed according to the characteristics of low speed collision of bumper system.Taking the peak collision force and the average collision force as two subsystems,a multidisciplinary collaborative optimization design is carried out,and its optimization results are compared with the ones optimized by NSGA-II algorithm.Simulation results show that the crashworthiness and energy absorption performance of the novel crash box is improved effectively based on the multidisciplinary optimization method.

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。

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.

Mechanical design and analysis of bio-inspired reentrant negative Poisson’s ratio metamaterials with rigid-flexible distinction

Aiming at achieving tunable reentrant structures with rigidity and uniformity,respectively,the C-shaped and S-shaped reentrant metamaterials were proposed by the bionic design of animal structures.Utilizing beam theory and energy methodology,the analytical expressions of the equivalent elastic modulus of the metamaterials were derived.Differences in deformation modes,mechanical properties,and energy absorption capacities were characterized by using experiments and the finite element analysis method.The effects of ligament angle and thickness on the mechanical characteristics of two novel metamaterials were investigated by using a parametric analysis.The results show that the stiffness,deformation mode,stress-strain curve,and energy absorption effects of three metamaterials are significantly different.This design philosophy can be extended from 2D to 3D and is applicable at multiple dimensions.

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.

Negative Poisson’s ratio cable compensation support for 32 m super-large-span highway tunnel:A case study

Although super-large-span tunnels ensure convenient transportation,they face many support challenges.The lack of normative construction guidance and the limited number of reference engineering cases pose a significant challenge to the stability control of superlarge-span tunnels.Based on the geological conditions of a super-large-span tunnel(span=32.17 m)at the bifurcation section of the Shenzhen interchange,this study determined support parameters via theoretical calculation,numerical simulation,and engineering analogy.The support effects of negative Poisson’s ratio(NPR)anchor cables and ordinary anchor cables on super-long-span tunnels were simulated and studied.Further,based on FLAC3D simulations,the surrounding rock stress field of NPR anchor cables was analyzed under different prestressing conditions,and the mechanism of a long-short combination,high-prestress compensation NPR anchor cable support was revealed.On the basis of numerical simulations,to our knowledge,the three-dimensional(3D)geomechanical model test of the NPR anchor cable and ordinary anchor cable support for super-large-span tunnel excavation is conducted for the first time,revealing the stress evolution law of super-large-span tunnels,deformation and failure characteristics of the surrounding rock,and the changing trend of the anchor cable’s axial force,and verifies that NPR anchor cables with high preloads are suitable for super-large-span tunnel support and have advantages over ordinary anchor cables.This study can provide a reliable theoretical reference for the support design and stability control of the surrounding rock of similar shallow-buried super-large-span tunnels.

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.

Parametric design strategy of a novel cylindrical negative Poisson's ratio jounce bumper for ideal uniaxial compression load-displacement curve

A cylindrical negative Poisson's ratio(CNPR) structure based on two-dimensional double-arrow negative Poisson's ratio(NPR)structure was introduced in this paper. The CNPR structure has excellent stiffness, damping and energy absorption performances,and can be applied as spring, damper and energy absorbing components. In this study, the CNPR structure was used as a jounce bumper in vehicle suspension, and the load-displacement curve of NPR jounce bumper was discussed. Moreover, the influences of structural parameters and materials on the load-displacement curve of NPR jounce bumper were specifically researched. It came to the conclusion that only the numbers of cells and layers impact the hardening displacement of NPR jounce bumper. And all parameters significantly affect the structure stiffness at different displacement periods. On the other hand, the load-displacement curve of NPR jounce bumper should be in an ideal region which is difficult to be achieved applying mathematical optimization method. Therefore, a parametric design strategy of NPR jounce bumper was proposed according to the parametric analysis results. The design strategy had two main steps: design of hardening displacement and design of stiffness. The analysis results proved that the proposed method is reliable and is also meaningful for relevant structure design problem.

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.

Innovative Thin-Walled Structure with Transverse Negative Poisson’s Ratio for High-Performance Crashworthiness

In this paper,an innovative type of thin-walled structures,the convex-concave honeycomb columns(CCHCs)with transverse negative Poisson’s ratio(NPR),is proposed for energy absorbers by replacing the cell walls of square honeycomb lattice columns with sine-shaped or zigzag-shaped walls of equal mass.Numerical simulations show that,under axial impact,contrary to the conventional square honeycomb columns of equal mass,the transverse cross section of NPR CCHC shrinks inward,making the cell walls of CCHC contact and interact sufficiently with each other and thus dissipate the impact energy much more effectively.By suitably adjusting the transverse NPR,the CCHC can have the combined advantages of effective total energy absorption,high specific energy absorption and low maximum peak crushing force.The research of this paper provides a new strategy for the design of high-performance energy absorbers widely used in the engineering fields of vehicle engineering,aerospace engineering etc.

Multi-objective robust design optimization of a novel negative Poisson's ratio bumper system

Negative Poisson's ratio(NPR) structure has outstanding performances in lightweight and energy absorption, and it can be widely applied in automotive industries. By combining the front anti-collision beam, crash box and NPR structure, a novel NPR bumper system for improving the crashworthiness is first proposed in the work. The performances of the NPR bumper system are detailed studied by comparing to traditional bumper system and aluminum foam filled bumper system. To achieve the rapid design while considering perturbation induced by parameter uncertainties, a multi-objective robust design optimization method of the NPR bumper system is also proposed. The parametric model of the bumper system is constructed by combining the full parametric model of the traditional bumper system and the parametric model of the NPR structure. Optimal Latin hypercube sampling technique and dual response surface method are combined to construct the surrogate models. The multi-objective robust optimization results of the NPR bumper system are then obtained by applying the multi-objective particle swarm optimization algorithm and six sigma criteria. The results yielded from the optimizations indicate that the energy absorption capacity is improved significantly by the NPR bumper system and its performances are further optimized efficiently by the multi-objective robust design optimization method.

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.

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.

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.

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.

Support principles of NPR bolt/cable and control techniques of large-deformation disasters

Deep mining has been paid much more attention because of the depletion of shallow mining resources.Traditional bolts could be invalid to accommodate large displacement and deformation in geomaterials.Consequently, alternative support and reinforcement bolts need to be studied and their constitutive models also need to be developed to help understanding for the complex stress-strain responses of rock masses under loadings. The effect of Negative Poisson's Ratio(NPR) that is attributed to the swelling phenomenon along the lateral direction may appear in metal materials under tensional loadings. Thence NPR materials often have an advantage over NPR ones in mechanical behavior such as impact resistance, antishearing, and energy absorbed. From the characteristics of NPR materials, a series of bolt and cable supports with the effect of NPR and constant-resistance have been recently developed. We here firstly introduce the structural features of NPR support. Then the constitutive model of NPR support is presented and its corresponding equation of energy equilibrium. Its basic principle interacted on rock masses is further discussed. Finally, NPR cables are employed to support the slope of an open-pit mine. The applications show that NPR cables can ease failure within the slope and play an important role in predicting and providing early warning of slope failure, together with a monitoring system of slope 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.