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.

Thermally insulating and fire-retardant bio-mimic structural composites with a negative Poisson's ratio for battery protection

Battery safety has attracted considerable attention worldwide due to the rapid development of wearable electronics and the steady increase in the production and use of electric vehicles.As battery failures are often associated with mechanical-thermal coupled behaviors,protective shielding materials with excellent mechanical robustness and flame-retardant properties are highly desired to mitigate thermal runaway.However,most of the thermal insulating materials are not strong enough to protect batteries from mechanical abuse,which is one of the most critical scenarios with catastrophic consequences.Here,inspired by wood,we have developed an effective approach to engineer a hierarchical nanocomposite via self-assembly of calcium silicate hydrate and polyvinyl alcohol polymer chains(referred as CSH wood).The versatile protective material CSH wood demonstrates an unprecedented combination of light weight(0.018 g cm-3),high stiffness(204 MPa in the axial direction),negative Poisson's ratio(-0.15),remarkable toughness(6.67×105 J m-3),superior thermal insulation(0.0204 W m-1 K-1 in the radial direction),and excellent fire retardancy(UL94-V0).When applied as a protective cover or a protective layer within battery packages,the tough CSH wood can resist high-impact load and block heat diffusion to block or delay the spread of fire,therefore significantly reducing the risk of property damage or bodily injuries caused by battery explosions.This work provides new pathways for fabricating advanced thermal insulating materials with large scalability and demonstrates great potential for the protection of electronic devices.

Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson's ratio

This paper proposes a three-dimensional(3D)Maltese cross metamaterial with negative Poisson’s ratio(NPR)and negative thermal expansion(NTE)adopted as the core layers in sandwich plates,and aims to explore the relations between the mechanical responses of sandwich composites and the NPR or NTE of the metamaterial.First,the NPR and NTE of the metamaterial are derived analytically based on energy conservation.The effective elastic modulus and mass density of the 3D metamaterial are obtained and validated by the finite element method(FEM).Subsequently,the general governing equation of the 3D sandwich plate under thermal environments is established based on Hamilton’s principle with the consideration of the von Kármán nonlinearity.The differential quadrature(DQ)FEM(DQFEM)is utilized to obtain the numerical solutions.It is shown that NPR and NTE can enhance the global stiffness of sandwich structures.The geometric parameters of the Maltese cross metamaterial significantly affect the responses of the thermal stress,natural frequency,and critical buckling load.

Switchable hidden spin polarization and negative Poisson's ratio in two-dimensional antiferroelectric wurtzite crystals

Two-dimensional(2D)antiferroelectric materials have raised great research interest over the last decade.Here,we reveal a type of 2D antiferroelectric(AFE)crystal where the AFE polarization direction can be switched by a certain degree in the 2D plane.Such 2D functional materials are realized by stacking the exfoliated wurtzite(wz)monolayers with“self-healable”nature,which host strongly coupled ferroelasticity/antiferroelectricity and benign stability.The AFE candidates,i.e.,Zn X and Cd X(X=S,Se,Te),are all semiconductors with direct bandgap atΓpoint,which harbors switchable antiferroelectricity and ferroelasticity with low transition barriers,hidden spin polarization,as well as giant in-plane negative Poisson's ratio(NPR),enabling the co-tunability of hidden spin characteristics and auxetic magnitudes via AFE switching.The 2D AFE wz crystals provide a platform to probe the interplay of 2D antiferroelectricity,ferroelasticity,NPR,and spin effects,shedding new light on the rich physics and device design in wz semiconductors.

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.

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.

Topological study about failure behavior and energy absorption of honeycomb structures under various strain rates

High-speed impact threats and terrorist actions on the battlefield require the development of more effective protective materials and structures,and various protective structure is designed according their energy-absorbing characteristics.In this research,the deformation behavior,microscopic failure modes and energy absorption characteristics of re-entrant hexagonal structure,regular hexagonal structure and regular quadrilateral structure are studied under different strain rates impact.The re-entrant hexagonal structure forms a“X”-shaped deformation zone,the regular quadrilateral and regular hexagonal structure form an“I”-shaped deformation zone.The microscopic appearance of the section is a mixed fracture form.The effects of the topological shape,cell angle,and cell height on the impact behavior of the structure were evaluated.When the cell height is fixed and the cell angle is changed,the energy absorption of the structure increase and then decrease as the relative density increase.The mechanical properties of the structure are optimal when the relative density is about 18.6%and the cell angle is22.5°.When the cell angle is fixed and the cell height is changed,as the relative density increases,the energy absorption of the structure gradually increases.The regular quadrilateral structure and the reentrant hexagonal structure experienced clear strain rate effects under dynamic impact conditions;the regular hexagonal structure did not exhibit obvious strain rate effects.The results presented herein provide a basis for further rational design and selection of shock-resistant protective structures that perform well in high-speed impact environments.

Mechanical enhancement and weakening in Mo_(6)S_(6)nanowire by twisting

The torsional,bending and tensile mechanical properties of Mo_(6)S_(6)nanowire are examined by molecular dynamics(MD)simulations with a first-principles-based reactive force field(ReaxFF).It is found that Mo_(6)S_(6)nanowire shows unique mechanical properties such as high torsional and bending flexibility,high Young's modulus and strength,and negative Poisson's ratio.The Mo_(6)S_(6)nanowire can be strengthened or weakened via twisting,depending on the twist angle.The Mo_(6)S_(6)nanowire with a slight twist angle shows brittle failure,whereas it with a large twist angle exhibits ductile failure and necking behavior.Twisted Mo_(6)S_(6)nanowires show a crossover in the negative Poisson's ratio at critical strains,that is,Poisson's ratio first decreases but then increases,with a minimum value down to around-0.8 at the strain of 0.01 as the twist angle is 21.0°/nm.The negative Poisson's ratio and the crossover are explained by the bond transform that makes zero angles to the wire cross-section.

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.

A new design of 3D-printed orthopedic bone plates with auxeticstructures to mitigate stress shielding and improve intra-operative bending

Orthopedic bone plates are most commonly used for bone fracture fixation for more than 100 years.The bone plate design had evolved over time overcoming many challenges such as insufficient strength and excessive plate–bone contact affecting the blood circulation.However,it is only made of two materials,either stainless steel(AISI 316L)or titanium(Ti–6Al–4V).There are two main limitations of metallic bone implants,namely stress shielding and the problem of malocclusion caused by the displacement of the fracture site during healing.To overcome the two problems,a new bone plate design with the incorporation of auxetic structures is proposed in this work.This study aims to use auxetic structure section in the bone plate that would decrease the stiffness of the region,thereby mitigating the stress-shielding effect and at the same time act as a deformable section to enable intra-operative bending for effective alignment while having enough bending strength and stiffness.Two different auxetic structures namely re-entrant honeycomb and missing rib structures were considered.The auxetic structure incorporated bone plates were designed,finite element analysis was done,fabricated using direct metal laser sintering technique,and tested.The results indicate that the re-entrant honeycomb structure incorporated bone plates serve as an effective bone design compared to the conventional bone plate design,in terms of stress shielding and intra-operative bending while offering similar mechanical and bending strength.

4D printing of personalized shape memory polymer vascular stents with negative Poisson’s ratio structure:A preliminary study

Four-dimensional(4D)printing,integrates transformation information into three-dimensional(3D)-printed structures,which means that 3D-printed structures are able to change their shapes,properties,or functionalities over time.Here,two types of shape memory personalized vascular stents with negative Poisson’s ratio structure are developed via 4D printing.The genetic algorithm is used to optimize the structure.Axial compression tests,radial compression tests and three-point bending tests are carried out to study the mechanical properties of the stents.In addition,fluid-structure interaction and stress distribution during the shape recovery process are investigated based on finite element method.The shape memory behaviors of the stents are excellent and in vitro feasibility tests demonstrate that the stents can expand the simulated narrow blood vessel rapidly.Therefore,4D printed shape memory stents with negative Poisson’s ratio structure are highly promising for the treatment of vascular stenosis.

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.

Modeling of deformation processes in rock massif in the vicinity of underground goafs considering the formation of discontinuity zones

The construction of mechanical-mathematical model and numerical method for the deformation processes of rock massifs with goafs and underground structures is very complex and also important task in modern rock mechanics.In this study,the mechanical-mathematical model is developed for rock massif in vicinity of underground goafs considering the internal block-layered structure of the rock massif.A new constitutive model is introduced in this study to describe the negative Poisson’s ratio for the lock-layered structure.Two types of defining equations systems for studying the state of a rock massif taking into account the block-layered structure are described.Finally,several examples are given using the present mechanical-mathematical model.

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.