Contact Problem Research Articles

Subsurface Stresses in Flat-Punch Contact Problems Including Friction

This work analyzes the influence of friction on the surface and subsurface contact stresses generated—in an elastic half-space—by a cylindrical flat-ended punch. For this purpose, the computational framework presented by [J. M. Juliá and L. Rodríguez-Tembleque, Subsurface stress evolution under orthotropic wear and frictional contact conditions, Int. J. Mech. Sci. 234 (2022) 107695] is extended to solve this problem. After the validation of this computational scheme, several numerical studies have allowed us to obtain the following conclusions. (i) The location of the maximum values of the subsurface Von Mises stresses in the [Formula: see text]–[Formula: see text] plane does not depend on the friction coefficient and is located at the contact zone limits — similarly to the normal pressure — (ii) However, the [Formula: see text]-location and the magnitude of the maximum value of the subsurface Von Mises stress is clearly affected by the values of the friction coefficient. (iii) The magnitude of the maximum value of the subsurface Von Mises stress increases and its location can be shifted from the subsurface region to the solid surface, when the friction coefficient increases its value.

АСИМПТОТИЧЕСКИЙ ПОДХОД К РЕШЕНИЮ КОНТАКТНОЙ ЗАДАЧИ ДЛЯ ТЕЛА КАЧЕНИЯ С ТОНКИМ ДЕФОРМИРУЕМЫМ ОБОДОМ

On the basis of an asymptotic approach to solving the elasticity theory boundary value problem for a thin strip rigidly linked to a non-deformable base, the differential equations are derived for determining the normal and shear loads distributed on the strip face free from fastening. These equations are used to solve the contact problem for a rigid cylinder with a thin elastic rim with a non-deformable horizontal rough support surface. The cylinder loading by a vertical force is considered for a given cylinder center settling. The calculated diagrams of contact pressure and shear contact stresses are obtained. In contrast to the previously used methods, the developed technique makes it possible to take into account the presence of adhesion and slip zones in the contact area, as well as to use a mathematically strict solution of the constitutive equations for contact pressure and shear contact stress. The value of the vertical force acting on the rigid cylinder for a given cylinder center displacement is determined. The stress tensor intensity distribution in the rim is established. The results of the developed technique application are compared with the calculated estimates obtained on the basis of the exact solution of the boundary value problem for a strip of arbitrary thickness and within the method, involving the use of the Winkler base simplified model. The dependences of the results error for the developed method on the thickness and Poisson's ratio of the rim material are obtained. The paper describes the effect of the rim-support surface friction coefficient on the contact pressure, shear contact pressure, and the maximum intensity of the stress tensor in the rim. It is concluded that it is reasonable to use the developed technique at solving contact problems for rolling elements with a relatively thin elastic rim.

Influence of Friction Coefficient between Cable and Membrane on Wind-Induced Response of Air-Supported Membrane Structures with Oblique Cable Net

Cable-membrane constructions typically exhibit significant displacement and distortion under load action, and the cable-membrane contact results in relative sliding. In this paper, the interaction force between cable and membrane is transferred through frictional contact action, and as a result, the friction coefficient must be taken into consideration for the form-finding and load analysis of air-supported membrane structures. Eight kinds of P-type membrane materials commonly used in engineering were chosen, and the friction coefficients between the various membrane and cable materials were obtained. The connection between a cable and a membrane of an air-supported membrane structure is considered a contact problem, and its initial shape analysis and wind load response analysis are carried out. The influence of the friction coefficient of a cable membrane on the wind-induced response of an air-supported membrane structure is discussed, and the results are compared with those of the cable-membrane binding model under wind load.

Analysis of numeric results for analogue of Galin’s problem in curvilinear coordinates

Purpose. Studying the results obtained when applying the perturbation method to the individual contact problems solution. Considering the influence of non-ideal material properties of interaction bodies. Considering the contact area’s complex geometry influence. Methodology. Mathematical models of the interaction of an elastic plate with cylindrical anisotropy in the form of a curvilinear sector problems have been constructed and considered. In the process of interaction between the stamp and the plate, areas of slippage and adhesion occur. The original complex problems of the theory of elasticity in the process of applying the perturbation method are reduced to the sequential solution of the potential theory problems. Findings. An analytical solution to the interaction of an elastic anisotropic plate in the form of a curvilinear sector and a rigid stamp problem was obtained considering the existence of slippage and adhesion areas in the contact area. Laws of stress distribution under the stamp were found, as well as dependence of this distribution on the dimensions of the contact area. Originality. The perturbation method is convenient and expedient to use when solving mining mechanics problems. The study on the stress-strain state of an elastic anisotropic plate for the analogue of Galin’s problem was carried out, and the corresponding analytical solutions were obtained. The dependence of the coupling area size on the dimensions of the stamp and the opening angle of the sector, physical properties of the material is analyzed. Possible boundary transitions have been completed. Practical value. The proposed approach makes it possible to obtain analytical solutions to practically important problems in mining, to evaluate the stress-strain state of thick-walled structures with reinforcing elements, stamps, overlays. The results can be useful when designing mine workings.

The virtual element method for general variational–hemivariational inequalities with applications to contact mechanics

This paper mainly analyzes the general elliptic variational–hemivariational inequalities with or without constraints by using the virtual element method. The approximations can be internal or external and a Céa’s type inequality is derived for a priori error estimates. Then, we apply the results to a variational–hemivariational inequality arising in frictional contact problems, and the optimal order error estimate is obtained for the linear virtual element solution under appropriate solution regularity assumptions. Finally, numerical simulation results are reported to show the performance of the proposed method, in particular, numerical convergence orders are in good agreement with the theoretical predictions.

Experimental Recognition of Plastic Domain in Contact Problem Based on Full Field Metrology and Neural Network

Contact usually results in stress concentration which can easily cause the yield of materials and structures. The classic elastic–plastic yield criterion needs to utilize stress or strain field for calculation. However, most advanced full-field measurement methods output the displacement as the original data, and the fitting from displacement to strain will induce error accumulation in applications. In this paper, a plastic domain characterization method is developed that can directly judge the elastic–plastic state of materials based on the full-field displacement and neural network. By establishing and training a three-layer-based neural network, the relationship between the displacement and the elastic/plastic stage of the sampling points is modeled. A physical model is formulated based on the yield criterion and embedded in the layer of the network, which can increase the convergence rate and accuracy. Only the displacements of the contact member are required in this method, which can be easily measured by the optical metrologies. The performances of the developed method are carefully discussed through simulated data and real-world tests. Results show that the method can accurately identify the plastic domain during the tests.

Developing a Fast-Processing Novel Algorithm for Contact Analysis of Standard Spur Gears

Numerical methods have gained momentum among specific engineering problems that must be solved in such a manner that accuracy and speed are the two most important aspects to consider regarding the output. This paper presents a fast, semi-analytical method (SAM) and original mathematical algorithms to determine the pressure distribution and von Mises stress for spur gears’ meshing teeth. The SAM begins with the Hartnett approach, based on Boussinesq’s equation for the half-space theory of linear elasticity, which implicitly means an infinite width of the gear flank. To simulate more realistic quarter-space conditions, corrections based on virtual mirror pressure are introduced in the computational algorithm. Mathematical surfaces modeling is an important aspect for spur gears as an intermediate stage to determine the pressure distribution and von Mises stress. Shaft misalignment changes the contact problem from symmetric, in which the half- or quarter-space model can be used, to asymmetric. In the latter case, the model must determine the entire contact area. The obtained output is validated by comparisons between our original FEA results and results from the literature using SAMs and FEA.

On the Possibility of Forming a Corium Pool by Induction Heating in a Melt Trap of the Lava-B Facility

This paper presents the results of computational and physical studies on the production of corium and its retention in an MR’s melt trap of the Lava-B facility. A feature of the Lava-B facility used in the IAE NNC RK to study the processes occurring during a severe accident at a nuclear reactor, is the separation of the stages of the reactor core corium formation and its interaction with structural materials. The melting of materials takes place in an induction furnace with a hot crucible, after which it moves to a melt receiver (MR) in which the test object is located. In the case of studies of processes occurring outside the reactor vessel, this is a special trap, which is placed in the inductor to simulate decay heat. However, based on the conservative computational estimates, it was found that the inductor power in the MR can be sufficient to directly produce, melt, and, subsequently, maintain the corium in the liquid phase. In this regard, in order to optimize the experiments under controlled conditions, the authors came up with the idea to experimentally test the possibility of producing corium by induction heating directly in the MR’s melt trap. In addition, according to the authors, this method would obviate the problem of corium contact with the carbon environment of the melting furnace of the Lava-B facility. Previously, burden heating simulating corium was modeled on the computer using available parameters of the MR’s induction heater. Based on the numerical experiment, the conditions for physical modeling of the corium production in the MR’s melt trap were established. An analysis of the physical modeling showed that during the burden heating in the melt trap, its metal components became liquid, thus, forming a melt pool. However, in terms of this design of the trap, there were problems associated with the complete melting of all corium components, as well as with the integrity of the experimental device when forming the corium pool and during the actual physical modeling.

A linear non-Hertzian unsteady tangential wheel-rail contact model

The increase in computational capacity has considerably reduced the use of linear models for wheel/rail tangential contact, being currently replaced by theories that adopt non-linear formulations able to address the most complex conditions realistically. However, linear formulations are difficult to replace in certain applications such as acoustic problem modelling, in which case a linear formulation of the track-contact-vehicle system is needed. The vibration that appears in this type of problem covers a wide range of audible frequencies, so, in addition to linearity, these theories are required to be non-stationary. The literature in contact mechanics gives response to this problem through models that consider low creepage levels, but it remains to cover other conditions in which the mean creepage is not small, such as when a railway vehicle negotiates a curve.This work presents a new theory of unsteady linear tangential rolling contact for non-Hertzian areas that considers kinematics as the sum of a constant creepage resulting from large stationary forces (such as those that occur when the vehicle negotiates a curve with constant radius) and small variable creepage due to a high-frequency phenomenon (e.g. the dynamic interaction between the vehicle and the track). The model is based on the Variational Theory (i.e. the CONTACT method for tangential problems), from which a linear formulation with variable creepage is deduced. According to this formulation, the non-steady state contact problem can be solved for any shape of the wheel/rail contact region, requiring a much smaller computational effort than the general unsteady CONTACT approach. The results show a satisfactory agreement of the proposed model to the unsteady CONTACT version, hence confirming the soundness of the proposed contact model.

A custom arc‐length Finite Element solver for large deformation adhesive contacts using a k‐d tree accelerated volumetric interaction scheme

AbstractThis paper introduces a Finite Element framework for large deformation adhesive contact between elastic bodies based on volume‐to‐volume interaction. A key component of this framework is a novel, customized arc‐length algorithm designed to follow the solution path through multiple snap‐through and snap‐back instabilities. Another new component is a k‐d tree based algorithm which significantly accelerates the computationally expensive volume‐to‐volume interaction calculations. This optimized Finite Element framework is then used to solve two‐body and three‐body elastic adhesive contact problems with realistic material and interaction parameters, using a 6‐12 Lennard‐Jones interaction potential. The improved efficiency of the k‐d tree based scheme makes it indispensable for interaction calculations. This paper also shows the importance of implementing adhesion‐specific customizations in the arc‐length solver.

ВЫХОД ШТОКА ТОРМОЗНОГО ЦИЛИНДРА РЫЧАЖНОЙ ПЕРЕДАЧИ ТЕПЛОВОЗОВ

The study objective is to develop a method for calculating the extension of the brake cylinder rod of a diesel locomotive. The extension value of the locomotive brake cylinder rod is currently not regulated, while the parameter is subject to control and must be consistent with the gaps between the brake shoe and the tyre. Its calculation involves taking into account the pressure in the cylinder, the cylinder diameter, the gear ratio of the lever transmission, the gaps between the shoe and the tyre, as well as the elastic deformation of the system. Currently, there is no method for determining the latter component, and this does not allow for a grounded choice of the brake cylinder at the design stage. In addition, increased wear of the brake shoes, for example, on a steep long descent, can lead to an insufficient rod extension. It is shown that significant exceedances of standard values are possible in operation. Thus, the extension of the brake cylinder rod of a diesel locomotive is an important parameter affecting traffic safety. The development of its calculation method is relevant. 
 It should be noted, that a significant contribution to the elastic component is made by wear-resistant bushings of lever transmission joints made of sintered iron-based materials. At the same time, the calculation of bushings is the most difficult.
 A method including the calculation of elastic deformation of levers and rods, as well as wear-resistant bushings by solving the contact problem of radial axis insertion into the wall of the sleeve is chosen as a prototype for the method of calculating the elastic component of the rod extension. This method is refined taking into account the features of the lever transmission. 
 The calculation of the rod extension for the lever transmission of the main diesel locomotive bogie is performed. At the moment, experimental data on the elastic component of the rod extension are obtained for it, and it gives the opportunity to evaluate the calculation results. The calculation of the rod extension showed good compliance with experimental measurements. The method can be used to select the appropriate brake cylinders for the locomotive lever transmission.

Numerical Analysis of Friction Reduction and ATSLB Capacity of Lubricated MTS with Textured Micro-Elements

The simulation analysis numerically investigates the thermoelastic lubricated interfacial Textured Micro-Element (TME) load-bearing contact, a theoretical model is proposed, and the effective friction reduction and Anti-Thermoelastic Scuffing Load bearing (ATSLB) capacity between random rough Meshing Teeth Surfaces (MTS) are presented, the mechanism linking interfacial thermoelastic lubrication, TME meshing friction reduction and ATSLB is revealed. The real contact domain area between MTS with multi-scale Micro-Element Textures (MET) is obtained for the numerical calculation of the three-dimensional equivalent TME contact volume, which is the correlation bridge between friction reduction and ATSLB of the thermoelastic lubrication interface. The proposed theoretical model predicts the time-varying behaviour of the textured meshing interface friction reduction with TME contact load under thermoelastic lubrication conditions. Numerical simulations show that the textured interface meshing volume is the key to solving the load-bearing problem of line contact between randomly rough teeth surfaces. The friction coefficients of the MTS are reduced by 13–24%. The lubricated load-bearing and friction reduction behaviour between the textured MTS is quantified by the thermoelastic voids of TME interface and actual meshing volume ratio, which provides a new perspective for further insight into the lubrication and friction reduction behaviour between the MTS with multi-scale MET-ATSLB coupling mechanism.

Wheel-rail contact and friction models: A review of recent advances

Rail transportation is regarded as a reliable, quick, and secure mode of transportation. The wheel-rail contact interaction is crucial to the railway operation since it is responsible for supporting, traction, braking, and steering of railway vehicles. Improper wheel-rail interactions may produce or exacerbate wheel-rail interface issues such as rolling contact fatigue (RCF) and wear, which can threaten the vehicle’s running safety and stability. A review of the evolution and recent literature on wheel-rail contact mechanics and tribology is presented here. Topics covered include the basics of wheel-rail contact problem and methodologies for modeling both the normal contact (Hertzian and non-Hertzian) and tangential contact (Kalker’s theories including CONTACT and FASTSIM algorithms, Polach’s theory, USETAB program, etc.). The paper also reviewed various effects of contaminants and environmental conditions (water, leaves, sand, temperature, humidity, etc.) in wheel-rail contact. Various wheel-rail empirical adhesion models like the Water-induced low adhesion creep force model (WILAC) model and adhesion models based on elastohydrodynamic lubrication (EHL) theory (Greenwood-Tripp [GT] and Greenwood-Williamson [GW] models) are also reviewed. Lastly, the paper discusses the need and challenges for developing and integrating the wheel-rail non-Hertz contact model and adhesion model, as well as open areas for further research.

Effect of inlet gas velocity on gas-solid fluidization characteristics in fluidized bed

Abstract In this article, the Eulerian–Eulerian TFM model is used to simulate the fluidization of the synthesis process of organosilicon monomers. A new method for analyzing the gas-solid fluidization characteristics is proposed by combining the gas-solid two-phase flow evolution formula with the parameters such as particle concentration and bed voidage. On this basis, the fluidization characteristics of silicon powder particles at constant velocity and variable velocity are compared, and the fluidization characteristics of silicon powder particles with different particle sizes under five sets of variable velocity are discussed. The simulation results show that compared with constant velocity, the mean bed voidage is 0.55 when silicon particles adopt variable velocity, which can not only keep silicon particles fully fluidized but also improve the problem of poor gas-solid contact. For silicon particles with particle diameters of 300.1–515 μm, variable velocity fluidization has the advantages of uniform bed distribution and sufficient gas-solid fluidization. In the five groups of variable velocity function, when the inlet gas velocity and time are the quadratic functions of the opening upward, the fluctuation of pressure fluctuation is small, and the maximum fluctuation range of particle solid phase distribution is only 0.13, indicating that the heat and mass transfer efficiency between silicon particles is better, the gas-solid mixing is sufficient, and the gas-solid fluidization quality is better.

A new class of fully history-dependent variational-hemivariational inequalities with application to contact mechanics

In this paper, we consider the behaviour of solutions to a class of fully history-dependent variational-hemivariational inequalities with respect to the perturbation of the data. First, the existence and uniqueness of the solution to a class of fully history-dependent variational-hemivariational inequalities is obtained by using a fixed point theorem. Second, we obtain continuous dependence result of solutions with respect to all the data of variational-hemivariational inequalities. Meanwhile, the convergence results of the solutions for the special case of abstract variational inequalities are also given. Finally, to illustrate our main results, we consider a class of viscoelastic contact problem with a long memory. By using our abstract result, we get the continuous dependence of the solutions to frictional contact problem with respect to all the data.

Weak solvability via bipotentials for contact problems with power-law friction

We study a bilateral contact model with power-law friction and a regularized version of it as well, a regularization of the friction law being considered. The behavior of the material is described by means of a subdifferential inclusion. We deliver a two-field variational formulation via bipotentials for the original problem and also for the regularized version. Subsequently, we study the solvability of the variational formulations we propose, based on abstract auxiliary results. Some properties of the solutions, paying attention to the data dependence, are also investigated. Finally, we deliver a convergence result.

Regularized frictional contact problems with the interior point method

The aim of this paper is to present an algorithm to solve frictional contact problems by considering the Coulomb’s criterion. As it is known, the frictional contact problem using Coulomb’s criterion has no minimization principle behind. However in order to use algorithms based on minimization methods, the frictional contact problem is written as an optimization one, more specifically as a sequence of Tresca contact problems. Moreover a family of regularization functions is introduced in order to regularize the non-smooth character of the Tresca criterion, which in some cases can have an experimental justifications. As each minimization problem becomes smooth enough, the interior point method is used to solve the generated optimization problem, which has some advantages when the non-penetration constraints are imposed in a symmetrical manner.

Specific Features of the Contact Interaction and Wear of Thin-Walled Structural Elements

We consider contact problems for thin-walled structural elements and their wear. We propose a unified method for solving the problems based on the reduction to Volterra integral equations. This enables us to detect singularities of solutions depending on the hypotheses characterizing the process of deformation of thin-walled elements. We present the solutions and analyze the problems of wear of the plates by a rigid punch and a hot punch with regard for the friction heating and changes in the thickness of the plate in the process of wear.

A contact description for continuum beams with deformable arbitrary cross-section

This work introduces a surface-to-surface contact description in the context of beam-to-beam contact. The introduced contact description is formulated in the frame work of the absolute nodal coordinate formulation. Leveraging the solid element-like features of the absolute nodal coordinate beam formulation and utilizing an interpolation scheme to parameterize the cross-section geometry, the computationally expensive discretization in beam’s thickness directions can be avoided. The developed formulation is general to account for internal and external contact scenarios. Numerical examples illustrate the robustness and applicability of the introduced formulation in contact problems comprising beams with arbitrary cross-sectional geometry and material nonlinearities. The numerical results indicate the effectiveness of the proposed contact solution to problems entailing various contact configurations, such as the presence of coupled large deformation modes within contact, contact between beams with sharp-edges, and a scenario where an arbitrary curve-to-curve contact takes place across beams’ surfaces. Accuracy of the contact integrals and the stability of the proposed formulation are also examined, respectively using the contact path and inf–sup tests. • Surface-to-surface contact is described for arbitrary cross-section beams. • The contact description involves large deformation modes and material nonlinearity. • Beam-inside-beam and sharp-edge contact interactions can be described. • Stability and accuracy of the contact integrals of the formulation are examined.

A new analytical-numerical model for contact problem counting asperities and strain hardening effects

The roughness effects on the wheel-rail contact problem is an essential topic. In this paper, a new analytical-numerical model has considered assessing the specifications of a rough surface contact problem. The new model includes asperities and strain hardening effects together. Consideration of these assumptions is more realistic in comparison to similar simplified works. In this work, the effects of material properties variation on a contact problem realize. Besides, considering the strain hardening effects, the contact results for wheel-rail material are obtained. The contact characteristics variations versus separation, such as contact force, contact stiffness, and contact area, are shown in semilogarithmic diagrams considering different surface roughnesses and hardening parameters. The new model results show the significant influence of the assumed hypothesis on the contact characteristics.