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.

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.

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.

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。

In-Plane and Out-of-Plane Mechanical Properties of Zero Poisson’s Ratio Cellular Structures for Morphing Application

Intelligent structures like zero Poisson’s ratio(ZPR)cellular structures have been widely applied to the engineering fields such as morphing wings in recent decades,owing to their outstanding characteristics including light weight and low effective modulus. In-plane and out-of-plane mechanical properties of ZPR cellular structures are investigated in this paper. A theoretical method for calculating in-plane tensile modulus,in-plane shear modulus and out-of-plane bending modulus of ZPR cellular structures is proposed,and the impacts of the unit cell geometrical configurations on in-plane tensile modulus,in-plane shear modulus and out-of-plane bending modulus are studied systematically based on finite element(FE)simulation. Experimental tests validate the feasibility and effectiveness of the theoretical and FE analysis. And the results show that the in-plane and out-of-plane mechanical properties of ZPR cellular structures can be manipulated by designing cell geometrical parameters.

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.

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.

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.

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.

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.

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.

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.

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.

鲁甸M_S6.5地震震源区地壳结构及孕震环境研究

本文利用由中国地震局在鲁甸地震震区附近架设的35个流动观测台站记录的远震事件记录,采用接收函数H-k扫描方法和CCP叠加成像方法获取了鲁甸地震震源区的地壳精细结构,结果显示鲁甸地震发生在地壳厚度和泊松比变化较剧烈的地区.昭通断裂西南段和东北段地壳物质组分差异明显,西南段断裂两侧地壳组分均显示为中泊松比分布,东北段断裂两侧泊松比从低泊松比快速变化为高泊松比,表明东北段西南侧壳内含有更多铁镁质组分,造成昭通断裂西南段和东北段对青藏高原下地壳物质向东南运移的阻挡有所差异,导致壳内应变积累,从而引起鲁甸地震的发生.在震源区地壳内部存在的低速层,可能为此次地震提供了可能的孕震环境.鲁甸地震与芦山地震虽然均没有产生明显的地表破裂带,但两者的震源机制以及孕震环境存在着明显的差异.本文也认为未来应关注青藏高原东缘断裂的历史地震空段发生大地震的可能性.本文研究结果对于理解青藏高原东缘区域的孕震背景具有一定的意义.

福建地区地壳上地幔S波速度结构与泊松比

利用在福建地区布置的12个宽频带数字地震流动台站和8个固定台站记录的远震P波波形数据进行接收函数计算,运用H-k搜索叠加方法得到了研究区的平均地壳厚度H与波速比k(=VP/VS),并运用接收函数反演方法得到了0～80km范围内的地壳和上地幔S波速度结构。H-k叠加结果表明,福建地区地壳厚度在28.4～32.8km范围内,从内陆到沿海变薄,从南到北变厚;沿着NW—SE方向,泊松比分布有分带特征,沿海地区泊松比高于内陆地区;同时表明,该地区地壳可分为上、中、下地壳,地壳结构横向差异较明显,多个台站下方可发现壳内低速层,沿海地区上地幔顶部平均速度相对低,可能暗示了深部存在热异常区域。

2022年1月8日青海门源M_(S)6.9地震深部构造背景浅析

2022年1月8日青海境内的托莱山—冷龙岭断裂附近发生了门源MS6.9地震。结合地壳厚度、速度结构及各向异性等资料探讨了门源地震的深部构造特征,揭示了门源地震的发震位置与地壳结构变化的密切关联。结果显示:门源MS6.9地震发生在地壳厚度和vP/vS值都出现快速空间变化的区域;大约在10—20 km深度范围内,震源位于P波速度从浅到深由高速变低速的垂向过渡区,同时也是S波速度和泊松比分布呈现明显横向变化的过渡区域,震源下方存在明显的低速区;冷龙岭断裂两侧相速度的方位各向异性变化比较明显。1月12日的MS5.2余震震中紧邻2016年MS6.4地震震中,揭示出2022年门源MS6.9地震及其余震活动导致了冷龙岭断裂比较充分的破裂,两次门源地震主震之间及邻区短时间内难以积累更大能量,因而短时间内发生更大地震的可能性不大。青藏高原东北缘的持续向北扩展所导致的地表隆升和地壳增厚是该地区强震频发的主要构造成因。