Finite element methods are used to study non-adhesive, frictionless contact between elastic solids with self-affine surfaces. We find that the total contact area rises linearly with load at small loads. The mean pressure in the contact regions is independent of load and proportional to the rms slope of the surface. The constant of proportionality is nearly independent of Poisson ratio and roughness exponent and lies between previous analytic predictions. The contact morphology is also analyzed. Connected contact regions have a fractal area and perimeter. The probability of finding a cluster of area ac drops as a −τ c where τ increases with decreasing roughness exponent. The distribution of pressures shows an exponential tail that is also found in many jammed systems. These results are contrasted to simpler models and experiment.

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This review summarizes recent advances in the area of tribology based on the outcome of a Lorentz Center workshop surveying various physical, chemical and mechanical phenomena across scales. Among the main themes discussed were those of rough surface representations, the breakdown of continuum theories at the nano-and micro-scales, as well as multiscale and multiphysics aspects for analytical and computational models relevant to applications spanning a variety of sectors, from automotive to biotribology and nanotechnology. Significant effort is still required to account for complementary nonlinear effects of plasticity, adhesion, friction, wear, lubrication and surface chemistry in tribological models. For each topic, we propose some research directions.

The adhesive wear process remains one of the least understood areas of mechanics. While it has long been established that adhesive wear is a direct result of contacting surface asperities, an agreed upon understanding of how contacting asperities lead to wear debris particle has remained elusive. This has restricted adhesive wear prediction to empirical models with limited transferability. Here we show that discrepant observations and predictions of two distinct adhesive wear mechanisms can be reconciled into a unified framework. Using atomistic simulations with model interatomic potentials, we reveal a transition in the asperity wear mechanism when contact junctions fall below a critical length scale. A simple analytic model is formulated to predict the transition in both the simulation results and experiments. This new understanding may help expand use of computer modelling to explore adhesive wear processes and to advance physics-based wear laws without empirical coefficients.

Calcite is among the most abundant minerals on earth and plays a central role in many environmental and geochemical processes. Here we used amplitude modulation atomic force microscopy (AFM) operated in a particular regime to visualize single ions close to the (1014) surface of calcite in solution. The results were acquired at equilibrium, in aqueous solution containing different concentrations of NaCl, RbCl, and CaCl(2). The AFM images provide a direct and atomic-level picture of the different cations adsorbed preferentially at certain locations of the calcite-water interface. Highly ordered water layers at the calcite surface prevent the hydrated ions from directly interacting with calcite due to the energy penalty incurred by the necessary restructuring of the ions' solvation shells. Controlled removal of the adsorbed ions from the interface by the AFM tip provides indications about the stability of the adsorption site. The AFM results show the familiar "row pairing" of the carbonate oxygen atoms, with the adsorbed monovalent cations located adjacent to the most prominent oxygen atoms. The location of adsorbed cations near the surface appears better defined for monovalent ions than for Ca(2+), consistent with the idea that Ca(2+) ions remain further away from the surface of calcite due to their larger hydration shell. The precise distance between the different hydrated ions and the surface of calcite is quantified using MD simulation. The preferential adsorption sites found by MD as well as the ion residence times close to the surface support the AFM findings, with Na(+) ions dwelling substantially longer and closer to the calcite surface than Ca(2+). The results also bring new insights into the problem of the Stern and electrostatic double layer at the surface of calcite, showing that parameters such as the thickness of the Stern layer can be highly ion dependent.

International audienceWe 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

A hybrid simulation method is introduced and used to study two-dimensional single-asperity and multi-asperity contacts both quasistatically and dynamically. The method combines an atomistic treatment of the interfacial region with a finite-element method description of subsurface deformations. The dynamics in the two regions are coupled through displacement boundary conditions applied at the outer edges of an overlap region. The two solutions are followed concurrently but with different time resolution. The method is benchmarked against full atomistic simulations. Accurate results are obtained for contact areas, pressures, and static and dynamic friction forces. The time saving depends on the fraction of the system treated atomistically and is already more than a factor of 20 for the relatively small systems considered here.

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