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Based on a potential theoretical approach, the subsurface stress field is calculated for an elastic half-space which is subject to normal and uniaxial tangential surface tractions that—in the case of elastic decoupling—correspond to rigid normal and tangential translations of a circular surface domain. The stress fields are obtained explicitly and in closed form as the imaginary parts of compact complex-valued expressions. The stress state in the surface and on the central axis are considered in detail. As, within specific approximations that have been discussed at length in the literature, any tangential contact problem with friction can be understood as a certain incremental series of such rigid translations, the solutions presented here can serve as the basis of very fast superposition algorithms for the analysis of subsurface stress fields in general tangential contact problems with friction. This idea is demonstrated by means of the frictional tangential contact between an elastic half-space and a rigid cylindrical flat punch with rounded corners. [ABSTRACT FROM AUTHOR]

Based on a potential theoretical approach, the subsurface stress field is calculated for an elastic half-space which is subject to normal and uniaxial tangential surface tractions that—in the case of elastic decoupling—correspond to rigid normal and tangential translations of a circular surface domain. The stress fields are obtained explicitly and in closed form as the imaginary parts of compact complex-valued expressions. The stress state in the surface and on the central axis are considered in detail. As, within specific approximations that have been discussed at length in the literature, any tangential contact problem with friction can be understood as a certain incremental series of such rigid translations, the solutions presented here can serve as the basis of very fast superposition algorithms for the analysis of subsurface stress fields in general tangential contact problems with friction. This idea is demonstrated by means of the frictional tangential contact between an elastic half-space and a rigid cylindrical flat punch with rounded corners.

In wheel-rail contact mechanics, there coexist different models characterised by their ability to reproduce the real phenomenon and the time associated with computing the solution. In simulation of the vehicle dynamics, the increase in the computational performance places researchers close to a horizon in which it is possible to implement the most realistic theories (Variational Theory or finite elements), although at present the use of these models is mainly limited to offline calculations, far from real-time simulation. In this context, this work presents a tangential contact theory that is an intermediate point between simplified models (unable to model non-Hertzian contact) and more realistic models (whose complexity triggers simulation times). The tangential contact model proposed is based on the FastSim algorithm, whose precision comes from the algorithm convergence to the results of an exact adhesion theory (i.e. when creepages tend to zero). The impossibility of considering Kalker's Linear Theory as an adjustment method when the hypotheses of the Hertzian model are not fulfilled leads to the adoption of the Kalker's steady-state CONTACT version in adhesion conditions. The calculations presented through the proposed algorithm provide errors for creep forces lower than 4% with computational times one order lower than the Variational Theory. [ABSTRACT FROM AUTHOR]

We present a formulation of the boundary element method (BEM) for simulating the tangential contact with an elastic half-space coated with an elastic layer with different elastic properties. We use the fast Fourier-transform-based formulation of BEM, while the fundamental solution is determined directly in the Fourier space. Numerical tests are validated by comparison with available asymptotic analytical solutions for a very thin and a very thick layer, as well as with FEM calculations for layers with finite thickness. [ABSTRACT FROM AUTHOR]

The dynamic behaviour of a railway vehicle is mainly depending on how the interaction of wheel and rail is taking place in running operation and what is the accuracy and efficiency of the applied contact models. Contact mechanics of railway vehicle is keyed with the history of the wheel-rail contact mechanics. For a designer of braking and traction control systems, it is essential to go through the fundamental knowledge of forces produced due to contact of wheel-rail and geometric constraints as well as moments to assess the wheel-rail wear and to evaluate the ride performance indices. This article gives a brief review to the evolution and present scenario of the previously published contact theories to get rid of the wheel-rail contact problems. The key theories which have most attention to solve normal contact problems are Hertzian contact theory as well as non-Hertzian contact theory, whereas, to tackle the problems related to tangential contact, linear as well as non-linear theories proposed by Kalker, theory proposed by Polach, FASTSIM, CONTACT etc are considered in this paper. This paper reviews the state-of-the-art of past studies based on experiments to study various contact models. [ABSTRACT FROM AUTHOR]

Due to the rapid development of additive manufacturing, a growing number of components in mechanical engineering are made of functionally graded materials. Compared to conventional materials, they exhibit improved properties in terms of strength, thermal, wear or corrosion resistance. However, because of the varying material properties, especially the type of in-depth grading of Young's modulus, the solution of contact problems including the frequently encountered tangential fretting becomes significantly more difficult. The present work is intended to contribute to this context. The partial-slip contact of axisymmetric, power-law graded elastic solids under classical loading by a constant normal force and an oscillating tangential force is investigated both numerically and analytically. For this purpose, a fictitious equivalent contact model in the mathematical space of the Abel transform is used since it simplifies the solution procedure considerably without being an approximation. For different axisymmetric shaped solids and various elastic inhomogeneities (types of in-depth grading), the hysteresis loops are numerically generated and the corresponding dissipated frictional energies per cycle are determined. Moreover, a closed-form analytical solution for the dissipated energy is derived, which is applicable for a breadth class of axisymmetric shapes and elastic inhomogeneities. The famous solution of Mindlin et al. emerges as a special case. [ABSTRACT FROM AUTHOR]

We present a formulation of the boundary element method (BEM) for simulating the tangential contact with an elastic half-space coated with an elastic layer with different elastic properties. We use the fast Fourier-transform-based formulation of BEM, while the fundamental solution is determined directly in the Fourier space. Numerical tests are validated by comparison with available asymptotic analytical solutions for a very thin and a very thick layer, as well as with FEM calculations for layers with finite thickness.

• Analyze canal frost heave characteristics and simplify its mathematical model. • Propose an analytical solution considering the normal and tangential interactions between the lining and frozen soil. • Propose calculation methods for determining the normal and tangential frost heave forces on structures. • Compare the proposed solution and traditional solution with two case histories. • The factors studied include the foundation coefficients, groundwater depth, canal size, and uplift displacement. Lined canals are important water suppliers and provide water for irrigation and other activities; however, they accumulate serious frost damage in cold regions. The frost heaving of frozen soil and its normal and tangential interactions with the canal lining are complex, which make it difficult to simplify analytical models; thus, research on analytical solutions for the response of canal lining under soil frost heaving are limited. First, trapezoidal canal frost heave characteristics were analyzed, and a new analytical solution based on the elastic foundation beam model considering tangential contact conditions at the lining–frozen soil interface was proposed. This solution is used to calculate the normal and tangential frost heave forces on the lining. Then, the proposed analytical solution and the traditional solution using an Euler beam on a Winkler foundation were compared with two case histories including field measurements and numerical simulations. The new solution agreed with the case histories and predicted the frost heave and stress of the lining, while the traditional solution neglecting tangential contact predicted only the normal lining frost heave, which was overestimated. Finally, the effects of the tangential and normal foundation coefficients, groundwater depth, canal size and uplift displacement at slope toes on canal frost heaving were investigated by parametric analysis. The proposed analytical solution can help engineers design canals using structural deformation and strength indexes and is applicable to frost heave response analyses of concrete face dams, slab foundations, culverts, and retaining walls. [ABSTRACT FROM AUTHOR]

Due to the rapid development of additive manufacturing, a growing number of components in mechanical engineering are made of functionally graded materials. Compared to conventional materials, they exhibit improved properties in terms of strength, thermal, wear or corrosion resistance. However, because of the varying material properties, especially the type of in-depth grading of Young’s modulus, the solution of contact problems including the frequently encountered tangential fretting becomes significantly more difficult. The present work is intended to contribute to this context. The partial-slip contact of axisymmetric, power-law graded elastic solids under classical loading by a constant normal force and an oscillating tangential force is investigated both numerically and analytically. For this purpose, a fictitious equivalent contact model in the mathematical space of the Abel transform is used since it simplifies the solution procedure considerably without being an approximation. For different axisymmetric shaped solids and various elastic inhomogeneities (types of in-depth grading), the hysteresis loops are numerically generated and the corresponding dissipated frictional energies per cycle are determined. Moreover, a closed-form analytical solution for the dissipated energy is derived, which is applicable for a breadth class of axisymmetric shapes and elastic inhomogeneities. The famous solution of Mindlin et al. emerges as a special case.

This study focusses on aiding the understanding of how various material properties affect rolling the contact fatigue (RCF) and wear of rail steels. This will support the future development of RCF prediction models, and in the identification of rail damage mechanisms. Tensile tests were conducted on several rail steel samples and compared to wear, and RCF data available in literature (Burstow, 2009), to try and meet the aim of this research. The findings from this study support the statements that hardness is a good indicator of ultimate tensile strength and that steel samples from the head and foot of rails have quite different yield strengths (max 24% difference). The strongest outcome of this research is data supporting claims that a ratio of the product of young’s modulus squared and percentage elongation to hardness cubed ((E2*Pe)/H3) had a much better correlation (R2=0.98) to wear data than just hardness (R2=0.89). As well as this, new ideas for characterizing Mark Burstow’s whole life rail model have been presented in this study, due to the importance of understanding how material properties impact rolling contact fatigue and wear. It is suggested in this study that the Tγ Threshold and Tγ Balance of a material could be calculated using ultimate tensile strength (UTS) and not hardness, due to findings showing a higher correlation between the number of cycles to RCF initiation and UTS (R2 = 1.0), than with hardness (R2 = 0.975).

The stress state in the volume of contacting bodies may essentially influence the material behavior. For evaluating various modes of inelastic behavior and/or failure, such as plastic deformation, crack initiation, and propagation or fatigue, the complete stress tensor beneath the contact interface may be of importance. For many geotechnical and biomechanical applications, the hydrostatic pressure gradient beneath the contact is of interest as well. However, most theories for normal and tangential contact provide only few stress components in the contact surface. In the present paper, we show that the full stress state in the half-space can be easily found for axisymmetric bodies. We provide expressions in form of one-dimensional integrals for all components of the stress tensor and the hydrostatic pressure gradient inside the half-space. In terms of numerical complexity, the proposed method can be advantageous to other elaborate methods.

The Hertzian contact theory, as well as most of the other classical theories of normal and tangential contact, provides displacements and the distribution of normal and tangential stress components directly in the contact surface. However, other components of the full stress tensor in the material may essentially influence the material behaviour in contact. Of particular interest are principal stresses and the equivalent von Mises stress, as well as the gradient of the hydrostatic pressure. For many engineering and biomechanical problems, it would be important to find these stress characteristics at least in the contact plane. In the present paper, we show that the complete stress state in the contact plane can be easily found for axially symmetric contacts under very general assumptions. We provide simple explicit equations for all stress components and the normal component of the gradient of hydrostatic pressure in the form of one‐dimensional integrals. [ABSTRACT FROM AUTHOR]

Fretting wear of axisymmetric contacts is considered within the framework of the Hertz–Mindlin approximation and the Archard law for the linear wear. If the characteristic time scale for the wear is much larger than the duration of a single fretting oscillation, the profile change due to wear during one fretting cycle can be neglected for the contact problem as a zero-order approximation. This allows to give an exact contact solution during each fretting cycle, depending on the current worn profile, and thus for the explicit statement of an ordinary integro-differential equation system for the time-evolution of the fretting profile, which can be easily solved numerically. The proposed method gives the same results as a known, contact mechanically more rigorous simulation procedure that also operates within the framework of the Hertz–Mindlin approximation, but works significantly faster than the latter one. Tangential and torsional fretting wear are considered in detail. A comparison of the numerical prediction for the evolution of the worn profile in partial slip torsional fretting of a rubber ball on abrasive paper shows good agreement with experimental results from the literature.

A transient FE model of wheelset-rail rolling contact has been developed with ANSYS/Ls-dyna to simulate the high speed running of a free wheelset on a slab track. Applying vertical, lateral and longitudinal vibrations at the passing frequencies of typical short pitch corrugation to the wheelset with no initial lateral shift, it is found that the vertical and lateral wheel-rail interactions are coupled to a large extent, while the longitudinal relatively independent under rolling-sliding and dependent when approaching full-sliding. The resulting irregular wear calculated with implemented wear models of Archard, Tγ and Zobory increases in amplitude with the friction exploitation level, whereas its phase keeps rather stable under rolling-sliding. As full-sliding is approached, the phase shifts greatly in the presence of the vertical or lateral vibration, but not of the longitudinal vibration. Consequently, corrugation initiation from the vertical and lateral vibrations becomes harder if both full- and rolling-sliding wheels pass over. • Distributed wear caused by transient frictional rolling contact is calculated in 3D. • The vertical and lateral wheel-rail interactions are coupled to a large extent. • The longitudinal interaction is relatively independent under rolling-sliding. • Corrugation is easier to initiate at high friction exploitation levels. • It is harder to initiate corrugation if both full- and rolling-sliding exist. [ABSTRACT FROM AUTHOR]

A three-dimensional contact between two linear elastically similar transversely isotropic solids of arbitrary geometry is considered. A simplified version of the classic Cattaneo-Mindlin theory, originally introduced by Ciavarella in the isotropic case, is developed under the assumption of complete decoupling of normal and tangential stress-displacement relations. Explicit tangential force-displacement relations are derived using Borodich’s self-similar transformations in the case of self-similar gap between the contacting surfaces. [ABSTRACT FROM AUTHOR]

In a nonsliding tangential contact, vectors of tangential force and tangential displacement are related by the tensor of tangential stiffness. Using the boundary element method, we calculate the principal values of the tensor of tangential stiffness for a number of contact shapes. Of special interest for applications is that the anisotropy of the tensor of tangential stiffness is generally relatively small, even for extremely anisotropic contact shapes. [ABSTRACT FROM AUTHOR]

The paper is concerned with the contact between the elastic bodies subjected to a constant normal load and a varying tangential loading in two directions of the contact plane. For uni-axial in-plane loading, the Cattaneo-Mindlin superposition principle can be applied even if the normal load is not constant but varies as well. However, this is generally not the case if the contact is periodically loaded in two perpendicular in-plane directions. The applicability of the Cattaneo-Mindlin superposition principle guarantees the applicability of the method of dimensionality reduction (MDR) which in the case of a uniaxial in-plane loading has the same accuracy as the Cattaneo-Mindlin theory. In the present paper we investigate whether it is possible to generalize the procedure used in the MDR for bi-axial in-plane loading. By comparison of the MDR-results with a complete three-dimensional numeric solution, we arrive at the conclusion that the exact mapping is not possible. However, the inaccuracy of the MDR solution is on the same order of magnitude as the inaccuracy of the Cattaneo-Mindlin theory itself. This means that the MDR can be also used as a good approximation for bi-axial in-plane loading. [ABSTRACT FROM AUTHOR]

Wheel–rail contact is more complex in railway a turnout than in ordinary track and, thus, necessitates an advanced model to simulate dynamic interaction and predict rail wear. The main aim of the present work is to assess the application of several wheel–rail rolling contact models in railway turnout. For normal contact problems, wheel–rail contact models based on four different methods are compared: Hertz theory, the semi-Hertzian method, CONTACT, and the finite element method. The assessment is based on the results of contact patch shape and size and contact pressure for several wheelset lateral displacements. The load is set to a constant and equal to static wheel load. Calculations are performed at the section of switch rail head with width 35 mm in CN60-1100-1:18 turnout; both standard and worn rail profiles are accounted for. For tangential contact problems, four corresponding methods are assessed, based on the calculation of creep forces, distribution of the stick/slide region and computational efficiency: Shen–Hedrick–Elkins theory, FASTSIM, improved FASTSIM based on semi-Hertzian method, and CONTACT. It is found that the normal contact problems solved by the semi-Hertzian method and CONTACT correlate well with the finite element method, and the tangential contact problems solved by improved FASTSIM and CONTACT are quite favorable. The conclusions of this work can provide some guidance for contact model selection in the dynamic simulation and wear prediction of railway turnout. [ABSTRACT FROM AUTHOR]

Until recently, the only way of solving contact problems was to apply three-dimensional contact theories. However, this presupposes higher mathematical and numerical knowledge, which usually only research groups possess. This has changed drastically with the development of the method of dimensionality reduction (MDR), which allows every practically oriented engineer an access to the solution of contact problems. The simple and contact-type dependent rules are summarized in the first part of the user manual; they require contacts between elastically homogeneous materials. The present paper forms the second part of the user handbook and is dedicated to the solution of contact problems between power-law graded materials. All the MDR-rules are listed with which normal, tangential and adhesive contacts between such high-performance materials can be calculated in a simple manner. [ABSTRACT FROM AUTHOR]

The method of dimensionality reduction is applied to the tangential contact between an elastomer and a rotationally symmetric indenter. The resulting equations are solved analytically, and numerical methods are discussed. The dependence of the normal and tangential force on the indentation depth and velocity is indicated. [ABSTRACT FROM AUTHOR]