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.

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In this paper, we show how the numerical theory introduced by the authors [Carbone and Putignano, J. Mech. Phys. Solids 61, 1822 (2013)] can be effectively employed to study the contact between viscoelastic rough solids. The huge numerical complexity is successfully faced up by employing the adaptive nonuniform mesh developed by the authors in Putignano et al. [J. Mech. Phys. Solids 60, 973 (2012)]. Results mark the importance of accounting for viscoelastic effects to correctly simulate the sliding rough contact. In detail, attention is, first, paid to evaluate the viscoelastic dissipation, i.e., the viscoelastic friction. Fixed the sliding speed and the normal load, friction is completely determined. Furthermore, since the methodology employed in the work allows to study contact between real materials, a comparison between experimental outcomes and numerical prediction in terms of viscoelastic friction is shown. The good agreement seems to validate-at least partially-the presented methodology. Finally, it is shown that viscoelasticity entails not only the dissipative effects previously outlined, but is also strictly related to the anisotropy of the contact solution. Indeed, a marked anisotropy is present in the contact region, which results stretched in the direction perpendicular to the sliding speed. In the paper, the anisotropy of the deformed surface and of the contact area is investigated and quantified.

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Classical lubrication theory is unable to explain a variety of phenomena and experimental observations involving soft viscoelastic materials, which are ubiquitous and increasingly used in e.g. engineering and biomedical applications. These include unexpected ruptures of the lubricating film and a friction-speed dependence, which cannot be elucidated by means of conventional models, based on time-independent stress-strain constitutive laws for the lubricated solids. A new modeling framework, corroborated through experimental measurements enabled via an interferometric technique, is proposed to address these issues: Solid/fluid interactions are captured thanks to a coupling strategy that makes it possible to study the effect that solid viscoelasticity has on fluid film lubrication. It is shown that a newly defined visco-elasto-hydrodynamic lubrication (VEHL) regime can be experienced depending on the degree of coupling between the fluid flow and the solid hysteretic response. Pressure distributions show a marked asymmetry with a peak at the flow inlet, and correspondingly, the film thickness reveals a pronounced shrinkage at the flow outlet; friction is heavily influenced by the viscoelastic hysteresis which is experienced in addition to the viscous losses. These features show significant differences with respect to the classical elasto-hydrodynamic lubrication (EHL) regime response that would be predicted when solid viscoelasticity is neglected. A simple yet powerful criterion to assess the importance of viscoelastic solid contributions to soft matter lubrication is finally proposed.