The Maugis analysis is applied to adhesive contact between a cylinder with various wave profiles and a semi-infinite, elastic half-plane. We extend the analysis of Waters, Lee and Guduru, who consider the adhesive contact of a Hertzian indenter on a semi-infinite, elastic half-space with axi-symmetric, wave profiles. This work gives the closed-form contact mechanical solution for continuous, line contact without the need for any approximation. The resulting semi-analytical model serves to complement existing (numerical) models of adhesive line contact with the static load-area response as a reference. Herewith we analyse adhesion-induced loading-unloading hysteresis and contrast semi-analytical and numerical result to assess the limit of the former analysis. We confirm that roughness-induced dissipation vanishes with increasing wave roughness and decreasing Maugis parameter due to an increase in the range of adhesion and cavitation. Instability and cavitation are mutually exclusive at a given load-area locus yet occur successively in the same contact. An interesting result is that the Johnson parameter, that is known to govern the amplification of adhesion in the JKR-limit, bounds the load-area envelope irrespective of Maugis parameter. However, the Johnson parameter does not control the occurrence of roughness-induced dissipation and thus interface toughening.

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Viscoelasticity and roughness are among the possible causes of the adhesive hysteresis displayed by soft contacts. Viscoelasticity causes an increased effective work of adhesion due to stiffening of the contact, while roughness is responsible for elastic instabilities. Herein, we explore the interplay between viscoelasticity and roughness by simulating in two dimensions the retraction of a rigid cylinder, with wavy surface profile, from a viscoelastic half-space. The wave amplitude and length are varied to induce instabilities in the load–to–area response, while the retraction velocity is increased to promote viscoelasticity. Results show that, in the regime where viscoelasticity is confined to the edges of the wavy contact, the contributions of viscoelasticity and waviness to adhesive hysteresis are nearly independent and additive. At low retraction rates, the instabilities in the load-area curve typical of rough elastic contacts are suppressed by viscoelasticity: the contact stiffens to promote a stable decrease of the contact area with load. This occurs with a minimal change in work of adhesion. However, when the instantaneous limit is met at high retraction rates, mechanical instabilities appear.

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The effect of the presence of a passivation layer on a metal rough surface during contact loading is investigated by means of dislocation dynamics simulations. The metal body is modeled as an FCC single crystal with a self-affine rough surface that is either bare, or covered by a thin coating, impenetrable to dislocations. This analysis permits to isolate the effect of surface roughening driven by dislocation motion: when the surface is bare the dislocations can glide out, leaving crystallographic steps at the surface that modify the local roughness; when the surface is passivated, dislocations are stopped by the interface.

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The small-scale topography of surfaces critically affects the contact area of solids and thus the forces acting between them. Although this has long been known, only recent advances made it possible to reliably model interfacial forces and related quantities for surfaces with multiscale roughness. This article sketches both recent and traditional approaches to their mechanics, while addressing the relevance of nonlinearity and nonlocality arising in soft- and hard-matter contacts. Graphical abstract: [Figure not available: see fulltext.].

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Discrete dislocation plasticity is a modeling technique that treats plasticity as the collective motion of dislocations. The dislocations are described through their elastic Volterra fields, outside of a cylindrical core region, with a few Burgers vectors of diameter. The contribution of the core fields to the dislocation dynamics is neglected, because it is assumed that their range is too short to be of influence. The aim of this work is to assess the validity of this assumption. In recent ab-initio studies it has been demonstrated that the dislocation core fields are significant up to a distance of ten Burgers vector from the dislocation line. This is a longer range influence than expected and can give rise to changes in the evolving dislocation structure and in the overall response of a plastically deforming body. It is indeed experimentally observed that dislocations pile up against strong interfaces, and that the spacing between dislocations at the front of these pile-ups can be less than ten Burgers vectors. In this work, 2-D discrete dislocation plasticity simulations are performed to investigate the effect of core fields on edge dislocation interactions. The results of the simulations, which include core fields for the first time, show indeed that dislocations that are very closely spaced experience additional glide or climb due to core fields. The effect is however negligible when compared to glide and climb due to Volterra fields or due to the external load.

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A seamless 2D dual-scale computational scheme is developed to study contact problems. The model consists of an atomistic domain close to the contact, coupled with an elastic continuum domain away from the contact. The atomistic formulation provides a description of the contact interaction through interatomic potentials and permits to capture atomic wear and defect formation in the contact region. The fields in the continuum domain are calculated by an efficient FFT-based Green's function method. The novel scheme is validated against full atomistic simulations and applied to study the effect of adhesion on the scratching of a rough copper surface by a rigid smooth spherical tip.

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The oscillation of a graphene flake on a substrate with undulated surface is investigated by classical molecular dynamics simulation. The gradient in amplitude of the undulation is found to provide the driving force for the motion of the graphene flake, which slides on top of a graphene layer that well conforms to the substrate. The oscillatory motion of the flake can be well described by the equation of motion of a damped oscillator, with damping factor corresponding to the friction coefficient between the flake and the graphene layer on which it glides. When the amplitude gradient increases, the oscillation frequency increases as well. The shape of the graphene flake is found to have a strong influence on friction, as some geometries promote in-plane rotation. The results in the present study point to an alternative approach to transport or manipulation of nanosized objects.

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It has been demonstrated through experiments and simulations that friction decreases significantly when graphene is used as a solid lubricant on various materials. However, the effect of increasing the number of graphene layers on lubrication is controversial. Some studies predict an increase of friction with the number of layers that can be imputed to increased contact area, others a decrease in friction attributed to increased flexural rigidity of the layers. Herein, atomistic simulations are performed to investigate the atomic mechanisms by which few-layers graphene lubricate rough copper surfaces when probed by a smooth tip. The results of the simulations show that increasing the number of graphene layers drastically reduces friction, while the deformation mechanism is found to change from atomic wear to recoverable flattening of surface steps, as the amount of interlocking between the surfaces is reduced.

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Graphene is well known as a solid lubricant for nanoscale devices and is generally used to decrease friction between flat surfaces. In this work, we investigate its performance as a lubricant for rough surfaces. To this end, the problem of a silicon tip sliding on a rough copper single crystal, bare or covered by a graphene layer, is addressed through molecular dynamics simulations. To simplify the analysis, the copper crystal is taken to be quasi-three dimensional, so that the roughness profile is constant along the short periodic dimension. Results show markedly different deformation mechanisms in copper, depending on whether the rough surface is bare, covered with a stretched graphene layer, or with a wrinkled graphene layer. The wrinkled layer appears to be the best solution to reduce friction.

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A model is proposed herein to investigate the incipient sliding of contacts in the presence of both friction and adhesion, where the interfacial response is modeled based on traction-separation laws. A Maugis-like parameter is defined to characterize the response in the tangential direction. Subsequently, the model is used to investigate the contact between a smooth cylinder and a flat body, where adhesion-friction interactions are strong. A range of behaviors are observed when a tangential displacement is imposed: When the parameter is low, the contact pressure exhibits a relatively constant profile; when it is high, a pressure spike is observed at the edge of the contact. This difference is caused by a significant interface compliance in the former case, which limits the amount of slip. The results for the mid-range values of the Maugis-like parameter can qualitatively replicate various experiments performed using polydimethylsiloxane (PDMS) balls.

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Contact between elastic bodies with self-affine rough surfaces is mostly studied with a focus on determining surface fields, despite body fields are of great importance to establish, for instance, when and where elasticity breaks down. This work aims at analyzing the effect of contact roughness on the body fields of compressible frictionless solids modeled using Green's function molecular dynamics. Although area-load curves are insensitive to changes in the Hurst exponent as long as they are correctly normalized and are clearly not affected by compressibility, the Von-Mises stress is found to depend on both Hurst exponent and Poisson's ratio.

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The retraction of a cylindrical rigid indenter from a viscoelastic substrate is studied by means of an efficient Green's function method. Hysteresis is observed in the load to area relationship in accordance with experimental results. Although our model relaxes many assumptions posed by LEFM-based analytical theories, the results fall between the limits, at high and low retraction velocities, predicted by the theories. Approaching the high velocity instantaneous limit requires, however, very high velocities or Maugis parameter. The work of adhesion is found to change during retraction. A non-dimensional parameter is proposed to estimate the effect of viscoelasticity in adhesive hysteresis.

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It is well established that, at small loads, a linear relation exists between contact area and reduced pressure for elastic bodies with non-adhesive rough surfaces. In the case of adhesive contacts, however, there is not yet a general consensus on whether or not linearity still holds. In this work evidence is provided, through numerical simulations, that the relation is non-linear. The simulations here presented can accurately describe contact between self-affine adhesive rough surfaces, since they rely on Green's function molecular dynamics to describe elastic deformation and on coupled phenomenological traction-separation laws for the interfacial interactions. The analysis is performed for two-dimensional compressible and incompressible bodies under plane strain conditions. Interfaces with various roughness parameters and work of adhesion are considered.

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One of the effective potentials that has proven to be very versatile and useful for describing metals is the modified embedded atom method (MEAM) potential. The reference-free version of the MEAM (RF-MEAM) potential provides more flexibility for fitting than the 2NN-MEAM because it also describes the pair potential as an explicit function. In this work, we present a methodology to fit RF-MEAM potentials to DFT data. We then evaluate the performance of the fitted potential by comparing MD simulations with experimental and DFT data. As an example, the methodology is applied to a binary and a quaternary alloy, namely NiTi and NbMoTaW. In the case of the equi-atomic NiTi shape memory alloy, our attention focuses on designing a potential that properly captures its mechanical behavior, given that the existing potentials fail to predict elastic constants in agreement with experiments. To reach our aim, we included the stress tensors of different high temperature NiTi configurations in the fitting database. The obtained RF-MEAM potential outperforms existing EAM and MEAM potentials in predicting the lattice and elastic constants of austenitic and martensitic phases as well as the corresponding transformation temperatures. To demonstrate the suitability of this methodology also for more complex systems, a RF-MEAM potential is fitted to model the multi-component NbMoTaW high-entropy alloy. Validation is achieved through comparison between observables obtained through the MD output and ab initio data. The article also reports key improvements to the optimization code MEAMfit v2 and the freely-available LAMMPS implementation of the RF-MEAM formalism. Most notably, resorting to analytic derivatives of the objective function with respect to the potential parameters rather than derivatives through finite differences, the time necessary for fitting has decreased by an order of magnitude.

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Experiments show that when an adhesive contact is subjected to a tangential load the contact area reduces, symmetrically or asymmetrically, depending on whether the contact is under tension or compression. What happens after the onset of sliding is more difficult to be assessed because conducting experiments is rather complicated, especially under tensile loading. Here, we provide through numerical simulations, a complete picture of how the contact area and tractions of an adhesive circular smooth punch evolve under mixed-mode loading, before and after sliding. First, the Green's function molecular dynamics method is extended to include the description of the interfacial interactions between contacting bodies by means of traction–separation constitutive laws that enforce coupling between tension (or compression) and shear. Next, simulations are performed to model sliding of a circular smooth punch against a flat rigid substrate, under tension and compression. In line with the experimental observations, the reduction in the contact area during shear loading is found to be symmetric under tension and asymmetric under compression. In addition, under tensile loading, full detachment is observed at the onset of sliding with a non-zero value of the tangential force. After the onset of sliding and the occurrence of slip instability, the contact area abruptly increases (reattachment), under both tension and compression. For interfaces with high friction, the reattachment occurs only partially. However, a full reattachment is attainable when friction is low.

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The contact mechanical response of various polymers is controlled by the viscoelastic behavior of their bulk and the adhesive properties of their interface. Due to the interplay between viscoelasticity and adhesion it is difficult to predict the contact response, even more when surfaces are rough. Numerical modeling could be of assistance in this task, but has so far mostly dealt with either adhesion or viscoelasticity and focused on simple geometries. Ideally, one would need a model that can concurrently describe viscoelasticity, surface roughness, and interfacial interactions. The numerical technique named Green's function molecular dynamics (GFMD) has the potential to serve this purpose. To date, it has been used to model contact between adhesive elastic bodies with self-affine surfaces. Here, as a first step, we extend the GFMD technique to include the transient contact response of frictionless viscoelastic bodies. To this end, we derive the constitutive equation for a viscoelastic semi-infinite body in reciprocal space, then integrate it using the semi-analytical method, and find the quasi-static solution through damped dynamics of the individual modes. The new model is then applied to study indentation as well as rolling of a rigid cylinder on a frictionless isotropic half-plane that follows the Zener model when loaded in shear. Extension of the method to a generalized viscoelastic model is straightforward, but the computational effort increases with the number of time-scales required to describe the material. The steady-state response of the rolling cylinder was provided analytically by Hunter in the sixties. Here, we use his analytical solution to validate the steady-state response of our model and provide additionally the transient response for bodies with various shear moduli.@en

During plastic deformation, metal surfaces roughen and this has a deleterious impact on their tribological performance. It is therefore desirable to be able to predict and control the amount of roughening caused by subsurface plasticity. As a first step, we focus on modelling plastic deformation during contact shearing of an FCC metallic single crystal, employing a finite strain Discrete Dislocation Plasticity (DDP) formulation. This formulation allows us to capture the finite lattice rotations induced in the material by shearing and the corresponding local rotation of the crystallographic slip planes. The simulations predict a pronounced material pile-up in front of the contact and a sink-in at its rear, which are strongly crystal-orientation dependent. By comparing finite and small strain DDP, we can assess the effect of slip plane rotation on surface roughening and on metal plasticity in general. Results of the simulations are also compared with crystal plasticity, which is also capable of predicting a pile-up and sink-in, but not the crystal-orientation dependency of roughening.

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Although indentation of elastic bodies by self-affine rough indenters has been studied extensively, little attention has so far been devoted to plasticity. This is mostly because modeling plasticity as well as contact with a self-affine rough surface is computationally quite challenging. Here, we succeed in achieving this goal by using Green's function dislocation dynamics, which allows to describe the self-affine rough surface using wavelengths spanning from 5 nm to 100μm. The aim of this work is to gain understanding in how plastic deformation affects the contact area, contact pressure and hardness, gap profile and subsurface stresses, while the roughness of the indenter is changed. Plastic deformation is found to be more pronounced for indenters with larger root-mean-square height and/or Hurst exponent, and to be size dependent. The latter means that it is not possible to scale observables, as typically done in elastic contact problems. Also, at a given indentation depth (interference) the contact area is smaller than for the corresponding elastic contact problem, but gap closure is more pronounced. Contact hardness is found to be much larger than what reported by classical plasticity studies. Primarily, this is caused by limited dislocation availability, for which the stiffness of the deforming crystal is in between that of a linear elastic and an elastic-perfectly plastic material. When calculating hardness and nominal contact pressure, including very small wavelength in the description of the surface is not necessary, because below a given wavelength the subsurface stresses become invariant to a further decrease in true contact area. This is true for both elastic and plastic materials. Considering small wavelengths is instead required to capture accurately roughening and contact stress distribution.

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Persson's theory allows for a fast and effective estimate of contact area and contact stress distributions when a flat and a self-affine rough surface are pressed into contact. For elastic bodies, the results of the theory have been shown to be in very good agreement with rather costly simulations. The theory has also been extended to plastic bodies. In this work, the results of Persson's theory for plastic bodies are compared with those of discrete dislocation plasticity. The area–load curves obtained by theory and simulations are found to be in good agreement when the rough surface has a very small root-mean-square (rms) height. For larger rms heights, which are more realistic for metal surfaces, the agreement is no longer good unless in the theory, instead of a size-independent material strength, one uses a rms height- and resolution-dependent yield strength. A modification of this type, i.e., the use of a yield strength dependent on size, does however not lead to agreement between the probability distributions of the contact stress, which is much broader in the simulations than in the theory. The most likely reason for this discrepancy is that the theory, apart from neglecting plasticity size dependence, only applies to elastic-perfectly plastic bodies and therefore, neglects strain hardening.

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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 microscales, 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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