EFFECT OF THE POISSON RATIO ON THE PERFECTLY PLASTIC STRESS FIELD AT A STATIONARY PLANE-STRAIN CRACK TIP

Under the condition that all the perfectly plastic stress components at a crack tip are the functions of ? only, making use of equilibrium equations and Von-Mises yield condition containing Poisson ratio, in this paper, we derive the generally analytical expressions of perfectly plastic stress field at a stationary plane-strain crack tip. Applying these generally analytical expressions to the concrete cracks, the analytical expressions of perfectly plastic stress fields at the stationary tips of Mode I, Mode II and Mixed-Mode I-II plane-strain cracks are obtained. These analytical expressions contain Poisson ratio.

Theoretical and Experimental Analyses of Poisson Ratios for Plain-Woven Fabrics

A theoretical model with extensible yarns for plain-woven fabrics is developed to determine the calculation of Poisson ratios.The stress ratio( warp: weft),as one of parameters corresponding to Poisson ratio variations, is introduced to complement the theoretical model. To evaluate the reliability of the theoretical analysis,a series of biaxial tensile tests of a plain-woven fabric with nine stress ratios are conducted carefully,and the theoretical results are compared with the experimentally measured values. The effects of other influencing factors, including geometric and mechanical parameters of yarns,on Poisson ratios are analyzed thoroughly.This solution method could be applied without difficulty to estimations of Poisson ratios and realistic designs for plain-woven fabrics.

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.

A gated recurrent unit model to predict Poisson’s ratio using deep learning

Static Poisson’s ratio(vs)is crucial for determining geomechanical properties in petroleum applications,namely sand production.Some models have been used to predict vs;however,the published models were limited to specific data ranges with an average absolute percentage relative error(AAPRE)of more than 10%.The published gated recurrent unit(GRU)models do not consider trend analysis to show physical behaviors.In this study,we aim to develop a GRU model using trend analysis and three inputs for predicting n s based on a broad range of data,n s(value of 0.1627-0.4492),bulk formation density(RHOB)(0.315-2.994 g/mL),compressional time(DTc)(44.43-186.9 μs/ft),and shear time(DTs)(72.9-341.2μ s/ft).The GRU model was evaluated using different approaches,including statistical error an-alyses.The GRU model showed the proper trends,and the model data ranges were wider than previous ones.The GRU model has the largest correlation coefficient(R)of 0.967 and the lowest AAPRE,average percent relative error(APRE),root mean square error(RMSE),and standard deviation(SD)of 3.228%,1.054%,4.389,and 0.013,respectively,compared to other models.The GRU model has a high accuracy for the different datasets:training,validation,testing,and the whole datasets with R and AAPRE values were 0.981 and 2.601%,0.966 and 3.274%,0.967 and 3.228%,and 0.977 and 2.861%,respectively.The group error analyses of all inputs show that the GRU model has less than 5% AAPRE for all input ranges,which is superior to other models that have different AAPRE values of more than 10% at various ranges of inputs.

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。

The Impact of Fabric Weave and Anisotropy on the Poisson’s Ratio in Technical Fabrics

Poisson’s ratio changes during the tensile stress of technical fabric samples due to the anisotropy of technical fabrics.This paper examines the effects of the type of weave and the anisotropic characteristics of the technical fabric on maximum tensile force,corresponding elongation,work-to-maximum force,elasticity modulus,and Poisson’s ratio when axial tensile forces are applied to samples cut at various angles in the direction of the weft yarns of the technical fabric.In the lab,3 cotton fabric samples of constant warp and weft density with different structural weave types(plain weave,twill weave,atlas weave)were subjected to the tensile force until they broke at the following angles:0°,15°,30°,45°,60°,75°,90°.Based on the different measured values of technical fabric stretching in the longitudinal direction and lateral narrowing,Poisson’s ratio is calculated.The Poisson’s ratio was calculated up to a relative elongation of the fabric of 8%,as the buckling of the fabric occurs according to this elongation value.According to the results presented in this paper,the type of weave of the fabric,the direction of tensile force,and the relative narrowing of the technical fabrics all play important roles in the Poisson’s ratio value.The Poisson’s ratio curve of a technical fabric under tensile stress(i.e.elongation)is primarily determined by its behaviour in the opposite direction of the elongation.The change in the value of the Poisson’s ratio is represented by a graph that first increases nonlinearly and then decreases after reaching its maximum value.

Effects of porosity on seismic velocities, elastic moduli and Poisson's ratios of solid materials and rocks

The generalized mixture rule(GMR) is used to provide a unified framework for describing Young’s(E),shear(G) and bulk(K) moduli, Lame parameter(l), and P- and S-wave velocities(Vpand Vs) as a function of porosity in various isotropic materials such as metals, ceramics and rocks. The characteristic J values of the GMR for E, G, K and l of each material are systematically different and display consistent correlations with the Poisson’s ratio of the nonporous material(v0). For the materials dominated by corner-shaped pores, the fixed point at which the effective Poisson’s ratio(n) remains constant is at v0=0.2, and J(G) > J(E) > J(K) > J(l) and J(G) < J(E) < J(K) < J(l) for materials with v0> 0.2 and v0< 0.2, respectively.J(Vs) > J(Vp) and J(Vs) < J(Vp) for the materials with v0> 0.2 and v0< 0.2, respectively. The effective n increases, decreases and remains unchanged with increasing porosity for the materials with v0< 0.2,v0> 0.2 and v0=0.2, respectively. For natural rocks containing thin-disk-shaped pores parallel to mineral cleavages, grain boundaries and foliation, however, the n fixed point decreases nonlinearly with decreasing pore aspect ratio(a: width/length). With increasing depth or pressure, cracks with smaller a values are progressively closed, making the n fixed point rise and finally reach to the point at v0=0.2.

Crustal Poisson's ratio anomalies in the eastern part of North China and their origins

Seismic tomography can provide both fine P-wave and S-wave velocity structures of the crust and upper mantle. In addition, with proper computation, Poisson＇s ratio images from the seismic velocities can be determined. However, it is unknown whether Poisson＇s ratio images have any advantages when compared with the P-wave and S-wave velocity images. For the purposes of this study, high- resolution seismic tomography under the eastern part of North China region was used to determine detailed 3-D crustal P- and S-wave seismic velocities structure, as well as Poisson＇s ratio images. Results of Poisson＇s ratio imaging show high Poisson＇s ratio （high-PR） anomalies located in the Hengshan-North Taihang-Zhangjiakou （H-NT-Z） region, demonstrating that Poisson＇s ratio imaging can provide new geophysical constraints for regional tectonic evolution. The H-NT-Z region shows a prominent and continuous high-PR anomaly in the upper crust. Based on Poisson＇s ratio images at different depths, we find that this high-PR anomaly is extending down to the middle crust with thickness up to about 26 kin. According to rock physical property measurements and other geological data, this crustal Poisson＇s ratio anomaly can be explained by Mesozoic partial melting of the upper mantle and basaltic magma underplating related to the lithospheric thinning of the North China craton.

Crustal thicknesses and Poisson's ratios beneath the Chuxiong-Simao Basin in the Southeast Margin of the Tibetan Plateau

In the Southeast Margin of the Tibetan Plateau, low-velocity sedimentary layers that would significantly affect the accuracy of the H-κ stacking of receiver functions are widely distributed.In this study, we use teleseismic waveform data of 475 events from 97 temporary broadband seismometers deployed by ChinArray Phase I to obtain crustal thicknesses and Poisson's ratios within the Chuxiong-Simao Basin and adjacent area, employing an improved method in which the receiver functions are processed through a resonance-removal filter, and the H-κ stacking is time-corrected.Results show that the crustal thickness ranges from 30 to 55 km in the study area, reaching its thickest value in the northwest and thinning toward southwest, southeast and northeast.The apparent variation of crustal thickness around the Red River Fault supports the view of southeastern escape of the Tibetan Plateau.Relatively thin crustal thickness in the zone between Chuxiong City and the Red River Fault indicates possible uplift of mantle in this area.The positive correlation between crustal thickness and Poisson's ratio is likely to be related to lower crust thickening.Comparison of results obtained from different methods shows that the improved method used in our study can effectively remove the reverberation effect of sedimentary layers.

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.

Design, Characterization, and 3D Printing of Cardiovascular Stents with Zero Poisson’s Ratio in Longitudinal Deformation

Inherent drawbacks associated with drug-eluting stents have prompted the development of bioresorbable cardiovascular stents.Additive manufacturing(3-dimentional(3D)printing)has been widely applied in medical devices.In this study,we develop a novel screw extrusion-based 3D printing system with a new designed mini-screw extruder to fabricate stents.A stent with a zero Poisson’s ratio(ZPR)structure is designed,and a preliminary monofilament test is conducted to investigate appropriate fabrication parameters.3D-printed stents with different geometric structures are fabricated and analyzed by observation of the surface morphology.An evaluation of the mechanical properties and a preliminary biological evaluation of 3D-printed stents with different parameters are carried out.In conclusion,the screw extrusion-based 3D printing system shows potential for customizable stent fabrication.

Modeling of Fatigue Crack Growth Closure Considering the Integrative Effect of Cyclic Stress Ratio,Specimen Thickness and Poisson's Ratio

Key components of large structures in aeronautics industry are required to be made light and have long enough fatigue lives.It is of vital importance to estimate the fatigue life of these structures accurately.Since the FCG process is affected by various factors,no universal model exists due to the complexity of the mechanisms.Most of the existing models are obtained by fitting the experimental data and could hardly describe the integrative effect of most existing factors simultaneously.In order to account for the integrative effect of specimen parameters,material property and loading conditions on FCG process,a new model named integrative influence factor model（IIF） is proposed based on the plasticity-induced crack closure theory.Accordingly to the predictions of crack opening ratio（γ） and effective stress intensity factor range ratio（U） with different material under various loading conditions,predictions of γ and U by the IIF model are completely identical to the theoretical results from the plane stress state to the plane strain state when Poisson＇s ratio equals 1/3.When Poisson＇s ratio equals 0.3,predictions of γ and U by the IIF model are larger than the predictions by the existing model,and more close to the theoretical results.In addition,it describes the influence of R ratios on γ and U effectively in the whole region from-1.0 to 1.0.Moreover,several sets of test data of FCG rates in 5 kinds of aluminum alloys with various specimen thicknesses under different loading conditions are used to validate the IIF model,most of the test data are situated on the predicted curves or between the two curves that represent the specimen with different thicknesses under the same stress ratio.Some of the test data slightly departure from the predictions by the IIF model due to the surface roughness and errors in measurement.Besides,based on the analysis of the physical rule of crack opening ratios,a relative thickness of specimen is defined to describe the influence of material property,specimen thickness and so forth on FCG characteristics conveniently.In conclusion,the relative thickness of specimen simplifies the expression of FCG characteristic and provides a general parameter to analyze the fatigue characteristics of different materials with various thicknesses under different loading conditions.The IIF model describes the integrative effect of existing influence factors explicitly and quantitatively,and provides a helpful tool for fatigue property estimation of practical component and experiment design.

Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson’s ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR’s implicit path dependence in addition to their separate intrinsic time reliance. Such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU intensive. Furthermore, there is no theoretical fundamental hint as to what loading path is required to produce a unique universal viscoelastic PR definition necessary for formulating a PR based constitutive relation or an EVCP protocol. The analysis associated with an additional Class VII viscoelastic PR establishes it as a universal representation which is loading path and strain independent while still remaining time dependent. This Class PR can be the one used if it is desired to express constitutive relations in terms of PRs, subject to the caveat applying to all PR Classes regarding the CPU intensiveness in the time space due to triple product and double convolution integral constitutive relations. However, the use PRs is unnecessary since any set of material behavior can be uniquely and completely defined in terms of only moduli and/or compliances. The mathematical model of instantaneous initial loading paths, based on Heavi-side functions, is examined in detail and shown to lead to infinite velocities and accelerations. Additionally, even if non-instantaneous gradual loading functions are employed the resulting PRs are still load and load history dependent. Consequently, they represent specialized PR responses applicable and limited to those particular load and history combinations. Although the analyses contained herein are generalized to non-homogeneous linear viscoelastic materials, the main focus is on PR time and process dependence. The non-homogeneous material results and conclusions presented herein apply equally to homogeneous viscoelasticity and per se do not influence the results or conclusions of the analytical development regarding viscoelastic PRs. In short, these PR analyses apply to all linear viscoelastic material characterization.

Effect of Poisson’s ratio on stress state in the Wenchuan M_S8.0 earthquake fault

The Wenchuan Ms8.0 earthquake occurred on the Longmenshan fault which inclines at a dip angle exceeding 60 degrees. Since most thrust earthquakes occur on faults with dip angles of about 30 degrees, it is enigmatic why the Wenchuan earthquake occurred on such a steep fault. In this study we use a simple finite element model to investigate how the stress state in the fault changes with the variation of Poisson＇s ratio. The results show that, with the Poisson＇s ratio in the fault increasing, the magnitudes of the principal stresses increase and the maximum Shear stress decrease, and, especially, the angle between the maximum principal stress and the fault plane decreases, which will enhance the driving force to overcome the frictional resistance on the fault. The increase of Poisson＇s ratio in the fault may be an important factor to affect the occurrence of the fault earthquakes with large angles between maximum principal stress and fault plane.

A note on influence of stress anisotropy on the Poisson's ratio of dry sand

In this study, extender and bender element tests were conducted investigating the small-strain Poisson’s ratio of variable sands, with a focus on the effect of stress anisotropy in order to quantify the sensitivity of Poisson’s ratio to the applied deviatoric stress. Four different uniform sands were tested, including a biogenic sand, a crushed rock and two natural sands, covering a wide range of particle shapes. From these sands, eleven samples were prepared in the laboratory and were tested under variable stress paths,maintaining a constant mean effective pressure while increasing the deviatoric compressive load. Under the application of these given stress paths, the data analysis indicated that the sensitivity of Poisson’s ratio to the stress ratio was more pronounced for sands with irregularly shaped particles in comparison to sands with fairly rounded and spherical grains. For sands with very irregularly shaped particles, the increase of Poisson’s ratio from the isotropic to the anisotropic stress state reached 50%, while this increase for natural sands with fairly rounded particles was in the order of 20%.

EFFECTS OF POISSON’S RATIO ON SCALING LAW IN HERTZIAN FRACTURE

In this paper the Auerbach＇s scaling law of Hertzian fracture induced by a spherical indenter pressing on a brittle solid is studied. In the analysis, the singular integral equation method is used to analyze the fracture behavior of the Hertzian contact problem. The results show that the Auerbach＇s constant sensitively depends on the Poisson＇s ratio, and the effective Auerbach＇s domain is also determined for a given value of the Poisson＇s ratio.

Topological Design of Microstructures of Materials Containing Multiple Phases of Distinct Poisson’s Ratios

A methodology for achieving the maximum bulk or shear modulus in an elastic composite composed of two isotropic phases with distinct Poisson’s ratios is proposed.A topology optimization algorithm is developed which is capable of finding microstructures with extreme properties very close to theoretical upper bounds.The effective mechanical properties of the designed composite are determined by a numerical homogenization technique.The sensitivities with respect to design variables are derived by simultaneously interpolating Young’smodulus and Poisson’s ratio using different parameters.The so-called solid isotropicmaterial with penalizationmethod is developed to establish the optimization formulation.Maximum bulk or shearmodulus is considered as the objective function,and the volume fraction of constituent phases is taken as constraints.Themethod ofmoving asymptotes is applied to update the design variables.Several 3D numerical examples are presented to demonstrate the effectiveness of the proposed structural optimization method.The effects of key parameters such as Poisson’s ratios and volume fractions of constituent phase on the final designs are investigated.A series of novel microstructures are obtained fromthe proposed approach.It is found that the optimized bulk and shearmoduli of all the studied composites are very close to the Hashin-Shtrikman-Walpole bounds.

The Crustal Thickness and Poissons Ratio Distribution in Guangdong and Its Adjacent Areas

Based on the teleseismic waveform data recorded by 82 permanent broadband stations in Guangdong Province and its adjacent areas including Fujian,Jiangxi,Hunan,Guangxi,Hainan and Taiwan,we calculate body wave receiver functions under all stations,and obtain the crustal thickness and average Poissons ratio beneath all stations by the H-κstacking-search method of receiver function. The results show that the crustal thickness with an average thickness of 29. 5km in Guangdong Province and its adjacent areas ranges between 26. 8km and 33. 6km and gradually thins from northwest to southeast. The crustal thickness in the Zhujiang Delta, western Guangdong, Nanning and Nanao areas is relatively thinner and ranges between 25. 0km and 28. 0km. The minimum crustal thickness is about 26 km beneath Wengtian, Hainan and the Zhanjiang zone and Shangchuan Island in Guangdong. The crustal thickness in the zones of Mingxi,Fujian and Yongzhou, Hunan is thicker and varies between 31. 0km and 34. 0km. The distribution of Poissons ratio in our study region ranges between 0. 20 and 0. 29. Poissons ratios in Southeast Hainan,the coastal areas of East Guangdong and West Fujian and the South Jiangxi have distinctly higher values than in others. It suggests that the various geothermal fields located in these areas have high heat flow values. The distribution of crustal thickness and Poissons ratio has an obvious block feature and may be related to the distribution of faults and historical earthquakes.

Study of crustal thickness and poisson's ratio of the south of Erenhot area by teleseismic receiver function

The Xing’an Mongolian Orogenic Belt(XMOB) and the northern margin of North China Craton(NCC) have undergone multistage tectonic superimposition and the tectonic evolution is extremely complicated. We collect the teleseismic data of 44 temporary broadband seismic stations deployed in the XMOB and the northern margin of NCC to calculate the P wave receiver functions. The crustal thickness and average crustal ratio as well as the Poisson’s ratios beneath 33 stations are estimated using the H-κ stacking method. The results show:(1) the crustal thickness of the study area ranges from 38.7 to 42.7 km, with an average thickness of 41.2 km. There is a great difference in crustal thickness on both sides of Solonker suture zone. The characteristics of crustal thickness support the geodynamic model that the Paleo-Asian Ocean subducted and closed at the Solonker suture zone.(2) The Poisson’s ratios in the study area are low, ranging from 0.215 to 0.277, with an average value of 0.243, suggesting that the rock composition of the area is dominated by felsic-acid rocks.(3) There exists a negative correlation between the Poisson’s ratio and the crustal thickness. Combined with the lower values of Poisson’s ratio, we speculate that the delamination is the major mechanism in crustal extension and thinning in the study area.

Characterization of the Crustal Thickness and Poisson's Ratio of the Binchuan Region

This paper presents the changes of crust thickness and Poissons ratios distribution in the Binchuan region,where the first air-gun transmitting station and its a small dense array were deployed.From September 2011 to January 2014,more than 239 teleseismic events of M≥6.0 were recorded in 16 stations in the Binchuan region.Their P-wave receiver functions were analyzed respectively.The high spatial resolution result shows that the average crust thickness of Binchuan region is 45.3km,it follows the rule of"deeper in the north and east part,shallower in the south and west part."The deepest region is in Xiaoyindian Station;the crust thickness is 47.9km;the shallowest region is in Paiying Station,it has the thickness of 42.1km.It shows that the deeper Moho surface nearby the Chenghai fault and shallower nearby the Honghe fault;the isoline distribution of thickness changes greatly nearby the Chenghai fault and slowly nearby the Honghe fault.From the distribution of Poissons ratios,it is unevenly in the study area with a great difference from the north part to the south part,which shows a characteristic of"lower in the north,higher in the south".The Poissons ratio nearby the Honghe fault is medium too high(0.26≤σ≤0.29);lower nearby the Chenghai fault(σ≤0.26).This paper concludes the possible reason of different characteristic between Poissons ratio and crust thickness is thicker in the upper crust in the Binchuan region.