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The non-conforming rolling contact under high loads results in considerable plastic deformation of the surface. This surface plastic flow is studied using a twin-disk tribometer, and the observed deformation as a function of the number of rolling cycles is classified into three distinct stages. Substantial geometric changes are observed in the initial stage and during this process, the contact type changed from Hertzian to non-Hertzian in the first few cycles, and then it changed from non-Hertzian back to near Hertzian by the end of this stage. A semi-analytical model is hence used to perform the contact analysis. Special traction elements are employed near the surface discontinuities within the contact area to resolve singularities. The contact area is observed to change from elliptic to a near-rectangular shape and the evolution of the contact parameters during this process is reported. Shakedown limits are obtained at different instants of the deformation process using Melan's theorem. It is observed that the high stresses near the surface discontinuities greatly affect the shakedown limits. The actual stress state is observed to move on a shakedown map until it goes below the shakedown limit but above the elastic limit as predicted. [ABSTRACT FROM AUTHOR]

We consider a quasistatic contact problem between a viscoelastic material with long-term memory and a foundation. The contact is modelled with a normal compliance condition, a version of Coulomb's law of dry friction and a bonding field which describes the adhesion effect. We derive a variational formulation of the mechanical problem and, under a smallness assumption, we establish an existence theorem of a weak solution including a regularity result. The proof is based on the time-discretization method, the Banach fixed point theorem and arguments of lower semicontinuity, compactness and monotonicity. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study a quasistatic contact problem between an electro-elastic viscoplastic body with damage and an electrically conductive foundation. The contact is modelled with an electrical condition, normal compliance and the associated version of Coulomb's law of dry friction in which slip dependent friction is included. We derive a variational formulation for the model and, under a smallness assumption, we prove the existence and uniqueness of a weak solution. [ABSTRACT FROM AUTHOR]

This paper presents an investigation into the effect of surface asperities on the over-rolling of bearing surfaces in transient elastohydrodynamic lubrication (EHL) line contact. The governing equations are discretized by the finite difference method. The resulting nonlinear system of algebraic equations is solved by the Jacobian-free Newton-generalized minimal residual (GMRES) from the Krylov subspace method (KSM). Acceleration of the GMRES iteration is accomplished by a wavelet-based preconditioner. Profiles of the lubricant pressure and film thickness are obtained at each time step when the indented surface moves through the contact region. The prediction of pressure as a function of time provides an insight into the understanding of fatigue life of bearings. The analysis confirms the need for the time-dependent approach of EHL problems with surface asperities. This method requires less storage and yields an accurate solution with much coarser grids. It is stable, efficient, allows a larger time step, and covers a wide range of parameters of interest. [ABSTRACT FROM AUTHOR]

The quasistatic normal-compliance contact problem of isotropic homogeneous linear visco-elastic bodies with Coulomb friction at small strains in Kelvin–Voigt rheology is considered. The discretization is made by a semi-implicit formula in time and the Symmetric Galerkin Boundary Element Method (SGBEM) in space, assuming that the ratio of the viscosity and elasticity moduli is a given relaxation-time coefficient. The obtained recursive minimization problem, formulated only on the contact boundary, has a nonsmooth cost function. If the normal compliance responds linearly and the 2D problems are considered, then the cost function is piecewise-quadratic, which after a certain transformation gets the quadratic programming (QP) structure. However, it would lead to second-order cone programming in 3D problems. Finally, several computational tests are presented and analysed, with an additional discussion on numerical stability and convergence of the involved approximated Poincaré–Steklov operators. [ABSTRACT FROM AUTHOR]

In this work, we use the homogenization theory to investigate the capability of wavy riblet patterns to influence the behaviour of a viscous flow near a ribbed boundary. Starting from perfect slip conditions on the wall, we show that periodic oscillations of wavy riblets in the lateral direction may induce a friction effect in the direction of the flow, contrary to what happens with straight riblets. Finally, we illustrate this effect numerically by simulating riblet profiles that are widely used in experimental studies: the V-shape, U-shape, and blade riblets. [ABSTRACT FROM AUTHOR]

The aim of this paper is to study an interaction law coupling recoverable adhesion, friction and unilateral contact between two viscoelastic bodies of Kelvin–Voigt type. A dynamic contact problem with adhesion and nonlocal friction is considered and its variational formulation is written as the coupling between an implicit variational inequality and a parabolic variational inequality describing the evolution of the intensity of adhesion. The existence and approximation of variational solutions are analysed, based on a penalty method, some abstract results and compactness properties. Finally, some numerical examples are presented. [ABSTRACT FROM AUTHOR]

The nonlocal friction law proposed by Oden et al. was adopted in order to consider the nonlocal friction effect of the asperities on the rough contact surface between the die and the workpiece in several kinds of metal plastic forming problems. The mechanical equilibrium equations with the integral-differential form were obtained by using the engineering method or slab method, and solved approximately by using the perturbation method. The normal stress distributions on the contact surfaces in metal forming problems with nonlocal friction were obtained, and the factors which affect the nonlocal friction effect were analyzed. [ABSTRACT FROM AUTHOR]