Vladislav Yastrebov

Sliding Without Slipping Under Coulomb Friction: Opening Waves and Inversion of Frictional Force

An elastic layer slides on a rigid flat governed by Coulomb’s friction law. We demonstrate that if the coefficient of friction is high enough, the sliding localizes within stick–slip pulses, which transform into opening waves propagating at intersonic speed in the direction of sliding or, for high Poisson’s ratios, at supersonic speed in the opposite direction. This sliding mode, characterized by marginal frictional dissipation, and similar to carpet fold propagation, may result in inversion of the frictional force direction; at longer time intervals, the system demonstrates stick–slip behavior. The mechanism is described in detail, and a parametric study is presented.

From infinitesimal to full contact between rough surfaces: Evolution of the contact area

We carry out a statistically meaningful study on self-affine rough surfaces in elastic frictionless non-adhesive contact. We study the evolution of the true contact area under increasing squeezing pressure from zero up to full contact, which enables us to compare the numerical results both with asperity based models at light pressures and with Persson’s contact model for the entire range of pressures. A good agreement of numerical results with Persson’s model is obtained for the shape of the area-pressure curve especially near full contact, however, we obtain qualitatively different results for its derivative at light pressures. We investigate the effects of the longest and shortest wavelengths in surface spectrum, which control the surface Gaussianity and spectrum breadth (Nayak’s parameter). We revisit the influence of Nayak’s parameter, which is frequently assumed to play an important role in mechanics of rough contact.

On the Propagation of Slip Fronts at Frictional Interfaces

The dynamic initiation of sliding at planar interfaces between deformable and rigid solids is studied with particular focus on the speed of the slip front. Recent experimental results showed a close relation between this speed and the local ratio of shear to normal stress measured before slip occurs (static stress ratio). Using a two-dimensional finite element model, we demonstrate, however, that fronts propagating in different directions do not have the same dynamics under similar stress conditions. A lack of correlation is also observed between accelerating and decelerating slip fronts. These effects cannot be entirely associated with static local stresses but call for a dynamic description. Considering a dynamic stress ratio (measured in front of the slip tip) instead of a static one reduces the above-mentioned inconsistencies. However, the effects of the direction and acceleration are still present. To overcome this, we propose an energetic criterion that uniquely associates, independently on the direction of propagation and its acceleration, the slip front velocity with the relative rise of the energy density at the slip tip.

Contact between representative rough surfaces

A numerical analysis of mechanical frictionless contact between rough self-affine elastic manifolds was carried out. It is shown that the lower cutoff wave number in surface spectra is a key parameter controlling the representativity of the numerical model. Using this notion we demonstrate that for representative surfaces the evolution of the real contact area with load is universal and independent of the Hurst roughness exponent. By introducing a universal law containing three constants, we extend the study of this evolution beyond the limit of infinitesimal area fractions.

The Contact of Elastic Regular Wavy Surfaces Revisited

Abstract We revisit the classic problem of an elastic solid with a two-dimensional wavy surface squeezed against an elastic flat half-space from infinitesimal to full contact. Through extensive numerical calculations and analytic derivations, we discover previously overlooked transition regimes. These are seen in particular in the evolution with applied load of the contact area and perimeter, the mean pressure and the probability density of contact pressure. These transitions are correlated with the contact area shape, which is affected by long range elastic interactions. Our analysis has implications for general random rough surfaces, as similar local transitions occur continuously at detached areas or coalescing contact zones. We show that the probability density of null contact pressures is nonzero at full contact. This might suggest revisiting the conditions necessary for applying Persson’s model at partial contacts and guide the comparisons with numerical simulations. We also address the evaluation of the contact perimeter for discrete geometries and the applicability of Westergaard’s solution for three-dimensional geometries.

On the accurate computation of the true contact-area in mechanical contact of random rough surfaces

We introduce a corrective function to compensate errors in contact area computations coming from mesh discretization. The correction is based on geometrical arguments, and apart from the contact area itself requires only one additional quantity to be computed: the length of contact/non-contact interfaces. The new technique enables to evaluate accurately the true contact area using a very coarse mesh, for which the shortest wavelength in the surface spectrum reaches the grid size. The validity of the approach is demonstrated for surfaces with different fractal dimensions and different spectral content using a properly designed mesh convergence test. In addition, we use a topology preserving smoothing technique to adjust the morphology of contact clusters obtained with a coarse grid.

The role of the roughness spectral breadth in elastic contact of rough surfaces

We study frictionless and non-adhesive contact between elastic half-spaces with self-affine surfaces. Using a recently suggested corrective technique, we ensure an unprecedented accuracy in computation of the true contact area evolution under increasing pressure. This accuracy enables us to draw conclusions on the role of the surface’s spectrum breadth (Nayak parameter) in the contact area evolution. We show that for a given normalized pressure, the contact area decreases logarithmically with the Nayak parameter. By linking the Nayak parameter with the Hurst exponent (or fractal dimension), we show the effect of the latter on the true contact area. This effect, undetectable for surfaces with poor spectral content, is quite strong for surfaces with rich spectra. Numerical results are compared with analytical models and other available numerical results. A phenomenological equation for the contact area growth is suggested with coefficients depending on the Nayak parameter. Using this equation, the pressure-dependent friction coefficient is deduced based on the adhesive theory of friction. Some observations on Persson’s model of rough contact, whose prediction does not depend on Nayak parameter, are reported. Overall, the paper provides a unifying picture of rough elastic contact and clarifies discrepancies between preceding results.

The existence of a critical length scale in regularised friction

We study a regularisation of Coulombs friction law on the propagation of local slip at an interface between a deformable and a rigid solid. This regularisation, which was proposed based on experimental observations, smooths the effect of a sudden jump in the contact pressure over a characteristic length scale. We apply it in numerical simulations in order to analyse its influence on the behaviour of local slip. We first show that mesh convergence in dynamic simulations is achieved without any numerical damping in the bulk and draw a convergence map with respect to the characteristic length of the friction regularisation. By varying this length scale on the example of a given slip event, we observe that there is a critical length below which the friction regularisation does not affect anymore the propagation of the interface rupture. A spectral analysis of the regularisation on a periodic variation of Coulombs friction is conducted to confirm the existence of this critical length. The results indicate that if the characteristic length of the friction regularisation is smaller than the critical length, a slip event behaves as if it was governed by Coulombs law. We therefore propose that there is a domain of influence of the friction regularisation depending on its characteristic length and on the frequency content of the local slip event. A byproduct of the analysis is related to the existence of a physical length scale characterising a given frictional interface. We establish that the experimental determination of this interface property may be achieved by experimentally monitoring slip pulses whose frequency content is rich enough.

A Local Contact Detection Technique for Very Large Contact and Self-Contact Problems: Sequential and Parallel Implementations

The local contact detection step can be very time consuming for large contact problems reaching the order of time required for their resolution. At the same time, even the most time consuming technique all-to-all does not guarantee the correct establishment of contact elements needed for further contact problem resolution. Nowadays the limits on mesh size in the Finite Element Analysis are largely extended by powerful parallelization methods and affordable parallel computers. In the light of such changes an improvement of existing contact detection techniques is necessary. The aim of our contribution is to elaborate a very general, simple and fast method for sequential and parallel detection for contact problems with known a priori and unknown master-slave discretizations. In the proposed method the strong connections between the FE mesh, the maximal detection distance and the optimal dimension of detection cells are established. Two approaches to parallel treatment of contact problems are developed and compared: SDMR/MDMR – Single/Multiple Detection, Multiple Resolution. Both approaches have been successfully applied to very large contact problems with more than 2 million nodes in contact.

Three-level multi-scale modeling of electrical contacts sensitivity study and experimental validation

An experimental and numerical study of electrical contact for low currents in sphere-plane set-up is presented. A three-level multi-scale model is proposed. We use the finite element analysis for macroscopic mechanical and electric simulations. It takes into account the setup geometry, elasto-plastic mechanical behavior of contacting components in the finite-strain-plasticity framework and electrostatic properties. A sensitivity analysis with respect to the brass plastic behavior and to the thickness of coating layers is also performed. The finite element results are used for an asperity-based model, which includes elasto-plastic deformation of asperities and their mutual elastic interactions. This model enables us to simulate the real morphology of contact spots at the roughness scale using the experimentally measured surface topography. Finally, the Greenwood multi-spot model is used to estimate the electrical contact resistance. This three-level model yields results which are in good agreement with experimental measurements carried out in this study.