Thermal-contact capacity of one-dimensional attractive Gaudin-Yang model

Tan's contact C is an important quantity measuring the two-body correlations at short distances in a dilute system.Here we make use of the technique of exactly solved models to study the thermal-contact capacity K_(T),i.e.,the derivative of C with respect to temperature in the attractive Gaudin-Yang model.It is found that K_(T) is useful in identifying the low temperature phase diagram,and using the obtained analytical expression of K_(T),we study its critical behavior and the scaling law.Especially,we show K_(T) versus temperature and thus the non-monotonic tendency of C in a tiny interval,for both spin-balanced and imbalanced phases.Such a phenomenon is merely observed in multi-component systems such as SU(2)Fermi gases and spinor bosons,indicating the crossover from the Tomonaga-Luttinger liquid to the spin-coherent liquid.

Calculation of high-speed abrasion forces for ceramic coatings based on the Hertzian contact model

Aero engine seal coatings can effectively improve the air tightness of aircraft engines and increase fuel efficiency.However,due to the frictional forces between the blades and the coating,the coating often flakes off,resulting in damage to the blades and causing eco-nomic losses.Therefore,it is necessary to analyze the friction between the blades and the coating.In this paper,three ceramic-based high-temperature seal coatings with different polyphenylene ester contents and a pure Yttria-stabilised zirconia coating were prepared by atmo-spheric plasma spraying(APS).The hardness and modulus of elasticity of the coated surfaces were obtained by hardness and modulus of elasticity tests,and the coatings were subjected to high-speed touch abrasion tests.The Hertzian contact model was used to calculate the maximum normal contact load on the coating during the process.The test values were compared with the theoretical values and it was found that the calculated values were always greater than the test values.In order to make the Hertzian contact model more accurate in calculating the touching and abrasion forces,the contact coefficients in the Hertzian contact model were optimized.Substituting the optimized coeffi-cients into the Hertzian contact model,the results show that the calculated results after optimizing the coefficients are much closer to the test values,with deviations from the test values ranging from 1%to 38%.

Stiffness and Shear Stress Distribution of Glulam Beams in Elastic-Plastic Stage:Theory,Experiments and Numerical Modelling

Traditional methods focus on the ultimate bending moment of glulam beams and the fracture failure of materials with defects,which usually depends on empirical parameters.There is no systematic theoretical method to predict the stiffness and shear distribution of glulam beams in elastic-plastic stage,and consequently,the failure of such glulam beams cannot be predicted effectively.To address these issues,an analytical method considering material nonlinearity was proposed for glulam beams,and the calculating equations of deflection and shear stress distribution for different failure modes were established.The proposed method was verified by experiments and numerical models under the corresponding conditions.Results showed that the theoretical calculations were in good agreement with experimental and numerical results,indicating that the equations proposed in this paper were reliable and accurate for such glulam beams with wood material in the elastic-plastic stage ignoring the influence of mechanic properties in radial and tangential directions of wood.Furthermore,the experimental results reported by the previous studies indicated that the method was applicable and could be used as a theoretical reference for predicting the failure of glulam beams.

An elastic-plastic contact model for line contact structures

Although numerical simulation tools are now very powerful,the development of analytical models is very important for the prediction of the mechanical behaviour of line contact structures for deeply understanding contact problems and engineering applications.For the line contact structures widely used in the engineering field,few analytical models are available for predicting the mechanical behaviour when the structures deform plastically,as the classic Hertz’s theory would be invalid.Thus,the present study proposed an elastic-plastic model for line contact structures based on the understanding of the yield mechanism.A mathematical expression describing the global relationship between load history and contact width evolution of line contact structures was obtained.The proposed model was verified through an actual line contact test and a corresponding numerical simulation.The results confirmed that this model can be used to accurately predict the elastic-plastic mechanical behaviour of a line contact structure.

Elastic-plastic contact force history and response characteristics of circular plate subjected to impact by a projectile

A new elastic-plastic impact-contact model is proposed in this paper. By adopting the principle of minimum acceleration for elastic-plastic continue at finite deformation, and with the aid of finite difference method, the proposed model is applied in the problem of dynamic response of a clamped thin circular plate subjected to a projectile impact centrally. The impact force history and response characteristics of the target plate is studied in detail. The theoretical predictions of the impact force and plate deflection are in good agreements with those of LDA experimental data. Linear expressions of the maximum impact force/transverse deflection versus impact velocity are given on the basis of the theoretical results.

Wheel-rail contact model for railway vehicle-structure interaction applications:development and validation

An enhancement in the wheel-rail contact model used in a nonlinear vehicle-structure interaction(VSI)methodology for railway applications is presented,in which the detection of the contact points between wheel and rail in the concave region of the thread-flange transition is implemented in a simplified way.After presenting the enhanced formulation,the model is validated with two numerical applications(namely,the Manchester Benchmarks and a hunting stability problem of a sus-pended wheelset),and one experimental test performed in a test rig from the Railway Technical Research Institute(RTRI)in Japan.Given its finite element(FE)nature,and contrary to most of the vehicle multibody dynamic commercial software that cannot account for the infrastructure flexibility,the proposed VSI model can be easily used in the study of train-bridge systems with any degree of complexity.The validation presented in this work proves the accuracy of the proposed model,making it a suitable tool for dealing with different railway dynamic applications,such as the study of bridge dynamics,train running safety under different scenarios(namely,earthquakes and crosswinds,among others),and passenger riding comfort.

Harten-Lax-van Leer-contact(HLLC)approximation Riemann solver with elastic waves for one-dimensional elastic-plastic problems

A Harten-Lax-van Leer-contact （HLLC） approximate Riemann solver is built with elastic waves （HLLCE） for one-dimensional elastic-plastic flows with a hypo- elastic constitutive model and the von Mises＇ yielding criterion. Based on the HLLCE, a third-order cell-centered Lagrangian scheme is built for one-dimensional elastic-plastic problems. A number of numerical experiments are carried out. The numerical results show that the proposed third-order scheme achieves the desired order of accuracy. The third-order scheme is used to the numerical solution of the problems with elastic shock waves and elastic rarefaction waves. The numerical results are compared with a reference solution and the results obtained by other authors. The comparison shows that the pre- sented high-order scheme is convergent, stable, and essentially non-oscillatory. Moreover, the HLLCE is more efficient than the two-rarefaction Riemann solver with elastic waves （TRRSE）

Contact Angle Prediction Model for Underwater Oleophobic Surfaces Based on Multifractal Theory

Traditional microstructure scale parameters have difficulty describing the structure and distribution of a roughmaterial’s surface morphology comprehensively and quantitatively. This study constructs hydrophilic and underwateroleophobic surfaces based on polyvinylidene fluoride (PVDF) using a chemical modification method, and the fractaldimension and multifractal spectrum are used to quantitatively characterize the microscopic morphology. A new contactangle prediction model for underwater oleophobic surfaces is established. The results show that the fractal dimension ofthe PVDF surface first increases and then decreases with the reaction time. The uniformity characterized by the multifractalspectrum was generally consistent with scanning electron microscope observations. The contact angle of water droplets onthe PVDF surface is negatively correlated with the fractal dimension, and oil droplets in water are positively correlated.When the fractal dimension is 2.0975, the new contact angle prediction model has higher prediction accuracy. Themaximum and minimum relative deviations of the contact angle between the theoretical and measured data are 18.20%and 0.72%, respectively. For water ring transportation, the larger the fractal dimension and spectral width of the materialsurface, the smaller the absolute value of the spectral difference, the stronger the hydrophilic and oleophobic properties, andthe better the water ring transportation stability.

Numerical Stability and Accuracy of Contact Angle Schemes in Pseudopotential Lattice Boltzmann Model for Simulating Static Wetting and Dynamic Wetting

There are five most widely used contact angle schemes in the pseudopotential lattice Boltzmann(LB)model for simulating the wetting phenomenon:The pseudopotential-based scheme(PB scheme),the improved virtualdensity scheme(IVD scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the fluid layer density above the wall(MPB-C scheme),the modified pseudopotential-based scheme with a ghost fluid layer constructed by using the weighted average density of surrounding fluid nodes(MPB-W scheme)and the geometric formulation scheme(GF scheme).But the numerical stability and accuracy of the schemes for wetting simulation remain unclear in the past.In this paper,the numerical stability and accuracy of these schemes are clarified for the first time,by applying the five widely used contact angle schemes to simulate a two-dimensional(2D)sessile droplet on wall and capillary imbibition in a 2D channel as the examples of static wetting and dynamic wetting simulations respectively.(i)It is shown that the simulated contact angles by the GF scheme are consistent at different density ratios for the same prescribed contact angle,but the simulated contact angles by the PB scheme,IVD scheme,MPB-C scheme and MPB-W scheme change with density ratios for the same fluid-solid interaction strength.The PB scheme is found to be the most unstable scheme for simulating static wetting at increased density ratios.(ii)Although the spurious velocity increases with the increased liquid/vapor density ratio for all the contact angle schemes,the magnitude of the spurious velocity in the PB scheme,IVD scheme and GF scheme are smaller than that in the MPB-C scheme and MPB-W scheme.(iii)The fluid density variation near the wall in the PB scheme is the most significant,and the variation can be diminished in the IVD scheme,MPB-C scheme andMPBWscheme.The variation totally disappeared in the GF scheme.(iv)For the simulation of capillary imbibition,the MPB-C scheme,MPB-Wscheme and GF scheme simulate the dynamics of the liquid-vapor interface well,with the GF scheme being the most accurate.The accuracy of the IVD scheme is low at a small contact angle(44 degrees)but gets high at a large contact angle(60 degrees).However,the PB scheme is the most inaccurate in simulating the dynamics of the liquid-vapor interface.As a whole,it is most suggested to apply the GF scheme to simulate static wetting or dynamic wetting,while it is the least suggested to use the PB scheme to simulate static wetting or dynamic wetting.

Finite Element Analysis of Elastic-Plastic Contact Mechanic Considering the Effect of Contact Geometry and Material Properties

Each surface of roughness has different shape of asperity which is modeled with various shapes of analytical models. In this paper, the differences among various models of shape of asperity investigate using the Finite Element Method (FEM) and various analytical models. The contact stresses in rough surfaces are calculated analytically using various asperity shape models. Finite element analysis is also carried out assuming three types of material properties namely, the linear, the elastic-perfect plastic and the elastic-nonlinear hardening. The analytical results are compared with the results obtained by the finite element method. The results illustrate for using a deterministic approach which the numerical models are suitable. In hertz model, the result of force is very big in interface of causing deformation plastic, while Model Zhao has almost same result with FEM nonlinear property model. It is observed that the results obtained from Zhao’s model are generally in a better agreement with the results obtained from various finite element models especially in elastic-plastic and plastic zones, hence it may be concluded that Zhao’s model can be used for analyzing the rough surfaces in contact mechanics.

A Finite Element Study of Elastic-Plastic Hemispherical Contact Behavior against a Rigid Flat under Varying Modulus of Elasticity and Sphere Radius

The present study considers a finite element analysis of elastic-plastic axi-symmetric hemispherical contact for a frictionless deformable sphere pressed by a rigid flat. The material of the sphere is modeled as elastic perfectly plastic. Analysis is carried out to study the effect of varying modulus of elasticity and sphere radius in wide range of dimensionless interference until the inception of plasticity as well as in plastic range. Results are compared with previous elastic-plastic models. It is found that materials with Young’s modulus to yield strength (E/Y) ratio less than and greater than 300 show strikingly different contact phenomena. The dependency of E on dimensionless interference at which the plastic region fully covers the surface is observed. However with different radius, finite element study exhibits similar elastic-plastic phenomena.

Heterogeneities of grain boundary contact for simulation of laboratoryscale mechanical behavior of granitic rocks

From a practical point of view,grain structure heterogeneities are key parameters that control the rock response and still remains a challenge to incorporate in a quantitative manner.One of the less discussed topics in the context of the grain-based model(GBM)in the particle flow code(PFC)is the contact heterogeneities and the appropriate contact model to mimic the grain boundary behavior.Generally,the smooth joint(SJ)model and linear parallel bond(LPB)model are used to simulate the grain boundary behavior.However,the literature does not document the suitability of different models for specific problems.Another challenge in implementing GBM in PFC is that only a single bonding parameter is used at the grain boundaries.The aim of this study is to investigate the responses of a laboratory-scale specimen with SJ and LPB models,considering grain boundary heterogeneous and homogeneous contact parameters.Uniaxial and biaxial compression tests are performed to calibrate the response of Creighton granite.The stressestrain curves,volumetric dilation,inter-crack(crack in the grain boundary),and intra-crack(crack within the grain)development,and failure patterns associated with different contact models are examined.It was found that both the SJ and LPB models can reproduce the pre-peak behavior observed for a granitic rock type.However,the LPB model is unable to reproduce the post-peak behavior.Due to the large interlocking effect originating from the balls in contact and the ball size in the LPB model,local dilation is induced at the grain boundaries.This overestimates the volumetric dilation and residual shear strength.The LPB model tends to result in discontinuous inter-cracks and stress localization in the rock specimen,resulting in fine fragments at the rock surface during failure.

Effect of contact materials on the transient characteristics of vacuum arc plasma and anode erosion

In this study, the mechanisms of the anode phenomena and anode erosion with various contact materials were investigated. Arc parameters were calculated, and the anode temperature was predicted with a transient self-consistent model. The simulation results predicted a constricted arc column and obvious anode phenomena in Cu–Cr alloy contacts than in W–Cu alloy contacts.This observation could be the reason for the concentrated anode erosion in Cu–Cr alloys. For the contacts made by pure tungsten(W) and W–Cu alloy, the anode temperature increased rapidly because of the low specific heat of W. However, the maximum energy flux from the arc column to the anode surface was lower than in other cases. The simulation results were compared with experimental results.

Experiment and constitutive modelling of creep deformation in the frozen silt-concrete interface

To ensure the long-term safety and stability of bridge pile foundations in permafrost regions,it is necessary to investigate the rheological effects on the pile tip and pile side bearing capacities.The creep characteristics of the pile-frozen soil interface are critical for determining the long-term stability of permafrost pile foundations.This study utilized a self-developed large stress-controlled shear apparatus to investigate the shear creep characteristics of the frozen silt-concrete interface,and examined the influence of freezing temperatures(−1,−2,and−5°C),contact surface roughness(0,0.60,0.75,and 1.15 mm),normal stress(50,100,and 150 kPa),and shear stress on the creep characteristics of the contact surface.By incorporating the contact surface’s creep behavior and development trends,we established a creep constitutive model for the frozen silt-concrete interface based on the Nishihara model,introducing nonlinear elements and a damage factor.The results revealed significant creep effects on the frozen silt-concrete interface under constant load,with creep displacement at approximately 2-15 times the instantaneous displacement and a failure creep displacement ranging from 6 to 8 mm.Under different experimental conditions,the creep characteristics of the frozen silt-concrete interface varied.A larger roughness,lower freezing temperatures,and higher normal stresses resulted in a longer sample attenuation creep time,a lower steady-state creep rate,higher long-term creep strength,and stronger creep stability.Building upon the Nishihara model,we considered the influence of shear stress and time on the viscoelastic viscosity coefficient and introduced a damage factor to the viscoplasticity.The improved model effectively described the entire creep process of the frozen silt-concrete interface.The results provide theoretical support for the interaction between pile and soil in permafrost regions.

Study of elastic-plastic damage model of cement consolidated soil with high organic content

On the basis of elastic-plastic damage model of cement consolidated soil,the authors took organic contents into reasonable damage variable evolution equation in order to seek relation between the organic contents and parameters in the equation,and established the elastic-plastic damage model of cement consolidated soil considering organic contents.The results show that the parameters change correspondingly with difference of the organic contents.The higher the organic contents are,the less the valves of the parameters such as elastic modulus(E),material parameters(K,n) and damage evolution parameter(ε) become,but the larger strain damage threshold value(εd) of the sample is.Meanwhile,the calculation results obtained from established model are compared with the test data in the condition of common indoors test,which is testified with reliability.

Fractal Prediction Model of Thermal Contact Conductance of Rough Surfaces

The thermal contact conductance problem is an important issue in studying the heat transfer of engineering surfaces, which has been widely studied since last few decades, and for predicting which many theoretical models have been established. However, the models which have been existed are lack of objectivity due to that they are mostly studied based on the statistical methodology characterization for rough surfaces and simple partition for the deformation formats of contact asperity. In this paper, a fractal prediction model is developed for the thermal contact conductance between two rough surfaces based on the rough surface being described by three-dimensional Weierstrass and Mandelbrot fractal function and assuming that there are three kinds of asperity deformation modes： elastic, elastoplastic and fully plastic. Influences of contact load and contact area as well as fractal parameters and material properties on the thermal contact conductance are investigated by using the presented model. The investigation results show that the thermal contact conductance increases with the increasing of the contact load and contact area. The larger the fractal dimension, or the smaller the fractal roughness, the larger the thermal contact conductance is. The thermal contact conductance increases with decreasing the ratio of Young＇s elastic modulus to the microhardness. The results obtained indicate that the proposed model can effectively predict the thermal contact conductance at the interface, which provide certain reference to the further study on the issue of heat transfer between contact surfaces.

Elastoplastic Contact Mechanics Model of Rough Surface Based on Fractal Theory

Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ~b, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.

Modeling and Calculation of Impact Friction Caused by Corner Contact in Gear Transmission

Corner contact in gear pair causes vibration and noise,which has attracted many attentions.However,teeth errors and deformation make it difficulty to determine the point situated at corner contact and study the mechanism of teeth impact friction in the current researches.Based on the mechanism of corner contact,the process of corner contact is divided into two stages of impact and scratch,and the calculation model including gear equivalent error-combined deformation is established along the line of action.According to the distributive law,gear equivalent error is synthesized by base pitch error,normal backlash and tooth profile modification on the line of action.The combined tooth compliance of the first point lying in corner contact before the normal path is inversed along the line of action,on basis of the theory of engagement and the curve of tooth synthetic complianceload-history.Combined secondarily the equivalent error with the combined deflection,the position standard of the point situated at corner contact is probed.Then the impact positions and forces,from the beginning to the end during corner contact before the normal path,are calculated accurately.Due to the above results,the lash model during corner contact is founded,and the impact force and frictional coefficient are quantified.A numerical example is performed and the averaged impact friction coefficient based on the presented calculation method is validated.This research obtains the results which could be referenced to understand the complex mechanism of teeth impact friction and quantitative calculation of the friction force and coefficient,and to gear exact design for tribology.

Contact Analysis and Modeling of Standing Wave Linear Ultrasonic Motor

A contact model for describing the contact mechanics between the stator and slider of the standing wave linear ultrasonic motor was presented. The proposed model starts from the assumption that the vibration characteristics of the stator is not affected by the contact process. A modified friction models was used to analyze the contact problems. Firstly, the dynamic normal contact force, interface friction force, and steady-state characteristics were analyzed. Secondly, the influences of the contact layer material, the dynamic characteristics of the stator, and the pre-load on motor performance were simulated. Finally, to validate the contact model, a linear ultrasonic motor based on in-plane modes was used as an example. The corresponding results show that a set of simulation of motor performances based on the proposed contact mechanism is in good agreement with experimental results. This model is helpful to understanding the operation principle of the standing wave linear motor and thus contributes to the design of these types of motor.

Influence of particle contact models on soil response of poorly graded sand during cavity expansion in discrete element simulation

The discrete element method(DEM) has been extensively adopted to investigate many complex geotechnical related problems due to its capability to incorporate the discontinuous nature of granular materials. In particular, when simulating large deformations or distortion of soil(e.g. cavity expansion),DEM can be very effective as other numerical solutions may experience convergence problems. Cavity expansion theory has widespread applications in geotechnical engineering, particularly to the problems concerning in situ testing, pile installation and so forth. In addition, the behaviour of geomaterials in a macro-level is utterly determined by microscopic properties, highlighting the importance of contact models. Despite the fact that there are numerous contact models proposed to mimic the realistic behaviour of granular materials, there are lack of studies on the effects of these contact models on the soil response.Hence, in this study, a series of three-dimensional numerical simulations with different contact constitutive models was conducted to simulate the response of sandy soils during cylindrical cavity expansion. In this numerical investigation, three contact models, i.e. linear contact model, rolling resistance contact model,and Hertz contact model, are considered. It should be noted that the former two models are linear based models, providing linearly elastic and frictional plasticity behaviours, whereas the latter one consists of nonlinear formulation based on an approximation of the theory of Mindlin and Deresiewicz. To examine the effects of these contact models, several cylindrical cavities were created and expanded gradually from an initial radius of 0.055 m to a final radius of 0.1 m. The numerical predictions confirm that the calibrated contact models produced similar results regarding the variations of cavity pressure, radial stress, deviatoric stress, volumetric strain, as well as the soil radial displacement. However, the linear contact model may result in inaccurate predictions when highly angular soil particles are involved. In addition, considering the excessive soil displacement induced by the pile installation(i.e. cavity expansion), a minimum distance of11 a(a is the cavity radius) is recommend for practicing engineers to avoid the potential damages to the existing piles and adjacent structures.