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.

Deformation Calculation of Cross-section Based on Virtual Force in Thin-walled Tube Bending Process

Cross-section deformation is one of important factors affecting the quality of tube formation, and the tube＇s capability of transporting liquid and gas will be reduced because of the cross-section ellipse deformation due to the effect of shear load in plastic bending process. When the tube is bent, the extrados-wall bears the tension stress and the intrados-wall bears the compression stress, synchronously the cross-section is affected by the circumferential stress. According to the above, the distribution function and curve of tangential stress can be obtained according to force balance differential equations on circumferential direction and Trasca rule. Subsequently the real state and virtual state moment equations were established, a new method was presented adopting the virtual principle of deformation system to calculate the x-axis and y-axis displacement of arbitrary point on cross-section. So the major and minor axes of deformed cross-section can be calculated according to the displacements of each point, and the variety value of major and minor axes will be obtained further. Finally the theoretical calculating result is compared with NC tube rotary-bending experiment results to verify the rationality of theoretical analysis, and the cross-section deformation rule of thin-walled tube can be received.

Microstructure and Property of High Carbonic-Chromium Cast Steel with Different Hot Deformation Ratio

The microstructure and properties of high carbonic-chromium cast steel subjected to different hot deformation ratios were studied.The experimental results show that the microstructure and properties of high carbonic-chromium cast steel are obviously improved after hot deformation,and the best mechanical properties of the cast steel can be obtained under hot deformation ratio of 40 %-50 %,which leads to the morphology change of eutectic carbide and the precipitation of granular carbides.

Experimental study of cross-section ratios in the collisions of C^(q+) and O^(q+) (q=1-4) on atomic helium in strong-interaction region

We have measured the cross-section ratios of helium induced by Cq＋ and Oq＋ （q = 1-4） in an energy range from 20 keV/amu to 500 keV/amu, and obtained the two-dimensional spectra by employing the coincidence method combined with the MPA-3 data acquisition system. Hence, we obtain the ratios of total single-ionization cross-sections （SI, SC, SLSI, and DLSI）, total double-ionization cross-sections （DI, DC, TI, SLDI, and DLDI） and cross-sections of every process （SI, SC, SLSI, DLSI, DI, DC, TI, SLDI, and DLDI）, which induce the single-ionization and double-ionization, to the total cross sections respectively. The competitive relations between the reaction-channels and the experimental data law of each reaction-channel are revealed explicitly, and the qualitative explanations involved in those results are also presented accordingly.

Elastic deformation of ellipsoidal shell of different axis ratio under inner pressure

Discusses the elastic deformation of ellipsoidal shell of different axis ratio under inner pressure during hydraulic bulging forming with theoretical results in good agreement with actual result, thereby providing theoretical basis for hydraulic bulging forming of ellipsoidal shell.

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.

Stability evaluation method of large cross-section tunnel considering modification of thickness-span ratio in mechanized operation

Purpose-This study aims to research the large cross-section tunnel stability evaluation method corrected after considering the thickness-span ratio.Design/methodology/approach-First,taking the Liuyuan Tunnel of Huanggang-Huangmei High-Speed Railway as an example and taking deflection of the third principal stress of the surrounding rock at a vault after tunnel excavation as the criterion,the critical buried depth of the large section tunnel was determined.Then,the strength reduction method was employed to calculate the tunnel safety factor under different rock classes and thickness-span ratios,and mathematical statistics was conducted to identify the relationships of the tunnel safety factor with the thickness-span ratio and the basic quality(BQ)index of the rock for different rock classes.Finally,the influences of thickness-span ratio,groundwater,initial stress of rock and structural attitude factors were considered to obtain the corrected BQ,based on which the stability of a large cross-section tunnel with a depth of more than 100 m during mechanized operation was analyzed.This evaluation method was then applied to Liuyuan Tunnel and Cimushan No.2 Tunnel of Chongqing Urban Expressway for verification.Findings-This study shows that under different rock classes,the tunnel safety factor is a strict power function of the thickness-span ratio,while a linear function of the BQ to some extent.It is more suitable to use the corrected BQ as a quantitative index to evaluate tunnel stability according to the actual conditions of the site.Originality/value-The existing industry standards do not consider the influence of buried depth and span in the evaluation of tunnel stability.The stability evaluation method of large section tunnel considering the correction of overburden span ratio proposed in this paper achieves higher accuracy for the stability evaluation of surrounding rock in a full or large-section mechanized excavation of double line high-speed railway tunnels.

A simple permanent deformation model of rockfill materials

Existing experimental results have shown that using a semi-log linear relationship between the permanent volumetric strain and cyclic number underestimates the volumetric deformation of rockfill materials with a large cyclic number, and that the error increases with the confining pressure. The existing permanent deformation models are not suitable for the seismic safety analysis of high dams during strong earthquakes. In this study, a series of large-scale triaxial cyclic loading tests of rockfill materials were performed, and a new permanent deformation model of rockfill materials was developed and validated with three kinds of rockfill materials. The results show that the proposed model can properly reflect the general features of the permanent deformation of rockfill materials. The main features of the model are as follows:(1) relations between the cyclic number and permanent volumetric/shear strain are described by hyperbolic functions, which can avoid underestimating the volumetric deformation occurring during strong earthquakes;(2) the model can capture the effect of the mean effective stress on the permanent volumetric strain, with greater confining pressure correlating to greater permanent volumetric deformation, and the permanent volumetric strain under low confining pressure near the dam crest can be well represented; and(3) the model can reflect the effect of the consolidation stress ratio on the permanent shear strain.

Aerodynamic effects on a railway tunnel with partially changed cross-sectional area

The present study numerically explored the aerodynamic performance of a novel railway tunnel with a partially reduced cross-section.The impact of the reduction rate of the tunnel cross-section on wave transmissions was analyzed based on the three-dimensional,unsteady,compressible,and RNG k-εturbulence model.The results highlight that the reduction rate(S)most affects pressure configurations at the middle tunnel segment,followed by the enlarged segments near access,and finally the exit.The strength of the newly generated compression wave at the tunnel junction where the cross-section abruptly changes increases exponentially with the decrease of the cross-sectional area.The maximum peak-to-peak pressureΔP on the tunnel and train surface for non-uniform tunnels is reduced by 10.7%and 13.8%,respectively,compared with those of equivalent uniform tunnels.Overall,the economic analysis suggests that the aerodynamic performance of the developed tunnel prototype surpasses those conventional tunnels based on the same excavated volume.

Role of stress,slenderness and foliation on large anisotropic deformations at deep underground excavations

High stress concentrations around underground excavations can result in significant damage to deep hard-rock mines.These conditions can be the result of stopping activities,blasting,seismicity,or other mining activities.Large anisotropic deformation and excavation closure,especially under high-stress conditions,are expected if the excavation is located in a foliated or thin-bedded rock mass.In this research,the behaviour of excavations under deep and high-stress conditions was investigated and categorised.The main purpose was to enhance the existing knowledge of managing large anisotropic deformations and to help prepare suitable measures for handling such contingencies.Numerical simulations using the distinct element method(DEM)and model calibration were performed to reproduce the anisotropic deformation of an ore drive based on the collected field data.Then,the roles of key factors(i.e.stress ratio,slenderness ratio,foliation orientation,and foliation considering excavation orientation)on the large deformation and damage depth of the excavations were investigated.This study found that increasing both the stress ratio and slenderness ratio induced linear increases in wall closure and damage depth,whereas increasing the foliation angle first increases the deformation and damage depth and then reduces them both before and after 45.The wall closure and damage thickness decreased with increasing orientation intercept.The deformation and damage levels were classified based on these factors.

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.

Rheology elasticity determined by deformation of stretchable molecular trains

The average stretching direction,local rotation angular,and stretching ratio parameters of molecular trains were used to express the rheology deformation.Based on this micro geometrical deformation,the macro deformation of medium was expressed.Then,using intrinsic elasticity concept,the stress-strain relation was obtained.In this theoretic formulation,the response functions of extension ratio and rotation angular were used to express the rheology feature of medium.For medium composed by incompressible molecular trains,the local rotation angular divides rheology deformation into three kinds:viscoelastic deformation or elasticity enhancement,viscoplastic deformation or elasticity degenerate and constant elasticity range.These results explain the experimental features of rheology deformation well.

Correlation between current and cross-sectional area of parallel fixed-movable dual electrodes in ESC

Electroslag casting with parallel fixed-movable dual electrodes is a new method for achieving better quality of castings in complex mold cavities.In this work,a mathematical model,y=kx^2+(k+1)x,was established to describe the ideal correlation between the current ratio(y)and the cross-sectional area ratio(x)of the dual electrodes,where k is the filling ratio.Investigation was conducted on the electroslag casting process with dual electrodes of various cross-sectional areas,but at a constant k value.The experimental results indicated that the ideal correlation was obtained at the stable casting stage,and the fitting results were consistent with the experimental results at certain k values.The experimental findings show that better castings can be obtained when the current ratio is greater than 1.536 and the cross-sectional area ratio is greater than 0.5.

Research of Elastic and Elastic-Plastic Deformation on Bending Problems of Variable Stiffness Beams

A novel variable stiffness model was proposed for analyzing elastic-plastic bending problems with arbitrary variable stiffness in detail.First,it was assumed that the material of a rectangular beam is an ideal isotropic elastic-plastic material,whose elastic modulus,yield strength,and section height are functions of the axial coordinates of the beam respectively.Considering the effect of shear on the deformation of the beam,the elastic and elastic-plastic bending problems of the axially variable stiffness beam were studied.Then,the analytical solutions of the elastic and elastic-plastic deformation of the beam were derived when the cross-section height and the elastic modulus of the material were varied by special function along the length of the beam respectively.The elastic and elastic-plastic analysis of the variable stiffness beam was carried out using Differential Quadrature Method(DQM)when the bending stiffness varied arbitrarily.The influence of the axial variation of the bending stiffness on the elastic and elastic-plastic deformation of the beam was analyzed by numerical simulation,DQM,and finite element method(FEM).Simulation results verified the practicability of the proposed mechanical model,and the comparison between the results of the solutions of DQM and FEM showed that DQM is accurate and effective in elastic and elastic-plastic analysis of variable stiffness beams.

High frequency doubling efficiency THz GaAs Schottky barrier diode based on inverted trapezoidal epitaxial cross-section structure

A high-performance terahertz Schottky barrier diode(SBD)with an inverted trapezoidal epitaxial cross-sectional structure featuring high varactor characteristics and reverse breakdown characteristics is reported in this paper.Inductively coupled plasma dry etching and dissolution wet etching are used to define the profile of the epitaxial layer,by which the voltage-dependent variation trend of the thickness of the metal-semiconductor contact depletion layer is modified.The simulation of the inverted trapezoidal epitaxial cross-section SBD is also conducted to explain the physical mechanism of the electric field and space charge region area.Compared with the normal structure,the grading coefficient M increases from 0.47 to 0.52,and the capacitance modulation ratio(C^(max)/C_(min))increases from 6.70 to 7.61.The inverted trapezoidal epitaxial cross-section structure is a promising approach to improve the variable-capacity ratio by eliminating the accumulation of charge at the Schottky electrode edge.A 190 GHz frequency doubler based on the inverted trapezoidal epitaxial cross-section SBD also shows a doubling efficiency of 35%compared to that 30%of a normal SBD.

Determination of mining-induced stresses using diametral rock core deformations

Knowledge of ground stresses is crucial for ground control activities such as the design of underground openings,selec-tion of support systems,and analysis for stability.However,it is a known fact that far field stresses experience changes in orientation and magnitude due to the presence of geological structures and due to the excavations created by mining activi-ties.As a result,in-situ stresses around drifts,ramps,and stopes in underground mines are quite different from far field or pre-mining stresses.The purpose of this research is to develop a simple and practical methodology for determining in-situ stresses.Stress relief occurs once the rock core is drilled off.Such relief is a function of the surrounding stress field.This study uses exploration rock cores that are drilled off for the purpose of orebody definition in the underground mine.The method measures and analyzes the diametral core deformations in laboratory.Two case studies from operating underground mines are presented for demonstration.In these case studies,rock core deformations are measured with a customized test apparatus and rock samples were prepared and tested for Young's modulus and Poisson's ratio.The differential stress,namely the difference between the local principal stresses in the plane perpendicular to the core rock axis is calculated.It is shown that this methodology is useful for determining the brittle shear ratio in the rock mass,which is of primary interest to ground control studies.

Characterisation of Early Age Deformations in Cement Paste: Case of Chemical and Autogenous Shrinkage

Concrete is commonly seen as a durable and long-lasting construction material. However, the long-term performance of a concrete structure can be greatly compromised by early-age cracking. This work is an experimental contribution to study early age deformations of cement paste. Its aim is, firstly, to develop an experimental dispositive for assessing chemical and autogenous shrinkage, and secondly, to measure these volumetric deformations in cement paste. The setup was done following the gravimetric method of measurement, which exploits the Archimedes’ principle. It is made up of an electronic balance, a data accusation unit, a temperature control unit and a buoyancy bath. Investigations were done on Portland cement (CPA-CEM II) at the following W/C ratios: 0.25, 0.3, 0.35, 0.4 and 0.5. It was noticed that the water-cement ratio does not influence the magnitude of the chemical shrinkage in a significant manner but had a kinetic effect;a lower W/C induces a faster rate of chemical shrinkage. Autogenous shrinkage was discovered to be highly inversely proportional to the W/C and was also noticed to be in a function of chemical shrinkage within the first 2 to 4 hours when the paste was still liquid.

Regional Tectonic Deformation Background and Medium- and Short-Term Precursors to the Minle-Shandan Earthquakes1

Using GPS observations of horizontal movement from 2001 to 2003 and the cross-fault mobile short-levelling data of 1988～2003, and with the aid of the improved negative dislocation model and the time-varying curve of strain intensity ratio of fault deformation, the regional tectonic deformation background and medium- and short-term precursors related to the preparation of the Minle-Shandan earthquakes of M S6.1 and M S5.8 on October 25, 2003 are investigated. The results reveal that, under the background of the wide-range deformation adjustment, short-term relaxation and recovery caused by the Kunlun Mountains earthquake of M S8.1, the hypocenters of the earthquakes are located on the north edge of the shear stress enhancement zone between the compressional locked segments of block boundary fault, a place which may represent an accelerated strain accumulation. An obvious anomaly of strain intensity ratio appeared in short-levelling measurements crossing over the fault at the Shihuiyaokou site, the closest to the epicenters, 3 months before the occurrence of the earthquakes. In addition, the variation in number of anomalies from 10-odd days to months before the earthquakes in the entire monitoring area and the anomaly concentration and local enhancement relative to near source in the 3 months before the earthquakes are regarded to be precursors to the two events.

Elliptical vibration chiseling:a novel process for texturing ultra-high-aspect-ratio microstructures on the metallic surface

High-aspect-ratio metallic surface microstructures are increasingly demanded in breakthrough applications,such as high-performance heat transfer enhancement and surface plasmon devices.However,the fast and cost-effective fabrication of high-aspect-ratio microstructures on metallic surfaces remains challenging for existing techniques.This study proposes a novel cutting-based process,namely elliptical vibration chiseling(EV-chiseling),for the high-efficiency texturing of surface microstructures with an ultrahigh aspect ratio.Unlike conventional cutting,EV-chiseling superimposes a microscale EV on a backward-moving tool.The tool chisels into the material in each vibration cycle to generate an upright chip with a high aspect ratio through material deformation.Thanks to the tool’s backward movement,the chip is left on the material surface to form a microstructure rather than falling off.Since one microstructure is generated in one vibration cycle,the process can be highly efficient using ultrafast(>1 kHz)tool vibration.A finite element analysis model is established to explore the process mechanics of EV-chiseling.Next,a mechanistic model of the microstructured surface generation is developed to describe the microstructures’aspect ratio dependency on the process parameters.Then,surface texturing tests are performed on copper to verify the efficacy of EV-chiseling.Uniformed micro ribs with a spacing of 1–10μm and an aspect ratio of 2–5 have been successfully textured on copper.Compared with the conventional EV-cutting that uses a forward-moving tool,EV-chiseling can improve the aspect ratio of textured microstructure by up to 40 times.The experimental results also verify the accuracy of the developed surface generation model of microstructures.Finally,the effects of elliptical trajectory,depth of cut,tool shape,and tool edge radius on the surface generation of micro ribs have been discussed.

基于数字图像相关技术的钢筋混凝土梁开裂特征量化研究

为研究配箍率对钢筋混凝土梁开裂特征的影响,依据我国规范设计了不同配箍率的钢筋混凝土梁,利用数字图像相关技术监测了钢筋混凝土梁试件在四点弯曲试验全过程,重现了不同级别荷载作用下试件的裂缝宽度及变形大小,并将试验结果与我国规范公式的计算结果进行对比。结果表明:数字图像相关技术能对全尺寸钢筋混凝土结构的裂缝及变形进行准确监测,钢筋混凝土梁在带裂缝工作阶段的裂缝宽度、间距均大于我国规范计算值,规范计算的裂缝宽度及间距均趋于保守,但我国规范可以对钢筋混凝土梁在带裂缝工作阶段的变形可以进行较好的预测。钢筋混凝土梁剪跨段裂缝分布及宽度受配箍率影响较大,纯弯段裂缝及宽度基本分布均匀,符合我国规范中裂缝计算公式的建立依据。