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This paper summarizes the submissions to a recently announced contact-mechanics modeling challenge. The task was to solve a typical, albeit mathematically fully defined problem on the adhesion between nominally flat surfaces. The surface topography of the rough, rigid substrate, the elastic properties of the indenter, as well as the short-range adhesion between indenter and substrate, were specified so that diverse quantities of interest, e.g., the distribution of interfacial stresses at a given load or the mean gap as a function of load, could be computed and compared to a reference solution. Many different solution strategies were pursued, ranging from traditional asperity-based models via Persson theory and brute-force computational approaches, to real-laboratory experiments and all-atom molecular dynamics simulations of a model, in which the original assignment was scaled down to the atomistic scale. While each submission contained satisfying answers for at least a subset of the posed questions, efficiency, versatility, and accuracy differed between methods, the more precise methods being, in general, computationally more complex. The aim of this paper is to provide both theorists and experimentalists with benchmarks to decide which method is the most appropriate for a particular application and to gauge the errors associated with each one.

We study the role of electronegativity in sliding friction for five different two dimensional(2D) monolayer systems using density functional theory (DFT) with van der Waals (vdW)corrections. We show that the friction between the commensurate 2D layered systems dependsstrongly on the electronegativity difference of the involved atoms. All the 2D layered structuresexhibit almost the same magnitude of friction force when sliding along the nonpolar path,independent of the material and the surface structures. In contrast, for sliding friction along thepolar path, the friction force obeys a universal linear scaling law as a function of theelectronegativity difference of its constituent atoms. Further analyses demonstrate that atomicdipoles in the 2D monolayers induced by the electronegativity difference enhance the corrugation ofcharge distribution and increase sliding barrier accordingly. Our studies revealthat electronegativity plays an important role in friction of low dimensional systems, and willprovide a strategy for designing nanoscale devices further.Keywords: Electronegativity; Friction; Two-dimensional (2D) monolayer; Density functionaltheory (DFT)

Most asteroids with a diameter larger than $\sim 300 \ {\rm m}$ are rubble piles i.e. consisting of more than one solid object. All asteroids are rotating but almost all asteroids larger than $\sim 300 \ {\rm m}$ rotate with a period longer than $2.3 \ {\rm hours}$, which is the critical period where the centrifugal force equals the gravitational force. This indicates that there are nearly no adhesive interaction forces between the asteroid fragments. We show that this is due to the surface roughness of the asteroid particles which reduces the van der Waals interaction between the particles by a factor of $100$ for micrometer sized particles and even more for larger particles. We show that surface roughness results in an interaction force which is independent of the size of the particles, in contrast to the linear size dependency expected for particles with smooth surfaces. Thus, two stone fragments of size $100 \ {\rm nm}$ attract each other with the same non-gravitational force as two fragments of size $10 \ {\rm m}$., 24 pages, 30 figures

We study the temperature and velocity dependency of rolling friction. Steel and PMMA cylinders are rolled on sheets of nitrile butadiene rubber (NBR), with and without filler, and fluoroelastomer (FKM) with filler. Measurements of the rolling friction are performed for temperatures between −40 °C and 20 °C, and for velocities between 5 μm s−1 and 0.5 cm s−1. For the unfilled NBR, a smooth rolling friction master curve is obtained using the bulk viscoelastic frequency–temperature shift factor aT. For the filled rubber compounds, a small deviation from the bulk viscoelastic shift factor is observed at low temperatures. The experimental data are analyzed using an analytical theory of rolling friction. For the filled compounds, good agreement with theory is obtained when strain softening is included, which increases the rolling friction by a factor ∼2 for the filled FKM and ∼3 for the filled NBR compounds. For the unfilled NBR, the maximum of the rolling friction occurs at higher sliding speeds than predicted by the theory. We discuss the role of the adhesive (crack-opening) contribution to the rolling friction, and the role of frozen-in elastic deformations as the rubber is cooled down below the rubber glass transition temperature.

We show that the Persson-Brener theory of crack propagation in viscoelastic solids gives a viscoelastic fracture energy factor $G/G_0 = 1+f$ which is nearly the same as the viscoelastic factor obtained using the cohesive-zone model. We also discuss finite-size effects and comment on the use of crack propagation theories for "solids" with a viscoelastic modulus that vanishes at zero frequency., 5 pages, 5 figures

Abstract Face masks are used to trap particles (or fluid drops) in a porous material (filter) in order to avoid or reduce the transfer of particles between the human lungs (or mouth and nose) and the external environment. The air exchange between the lungs and the environment is assumed to occur through the face mask filter. However, if the resistance to air flow through the filter is high some air (and accompanied particles) will leak through the filter-skin interface. In this paper I will present a model study of the side-leakage problem. Graphicabstract

I consider fluid flow at the interface between solids with random roughness. For anisotropic roughness, obtained by stretching isotropic roughness in the x-direction by a factor of $$\gamma ^{1/2}$$ γ 1 / 2 and in the y-direction with a factor of $$\gamma ^{-1/2}$$ γ - 1 / 2 , I give an argument for why the flow conductivity in the critical junction theory should be proportional to $$\gamma $$ γ in the x-direction and proportional to $$1/\gamma $$ 1 / γ in the y-direction.

We present experimental results for the dependency of the pull-off time (failure time) on the pull-off force for suction cups in the air and in water. The results are analysed using a theory we have developed for the contact between suction cups and randomly rough surfaces. The theory predicts the dependency of the pull-off time (failure time) on the pull-off force, and is tested with measurements performed on suction cups made from a soft polyvinyl chloride (PVC). As substrates we used sandblasted poly(methyl methacrylate) (PMMA). The theory is in good agreement with the experiments in air, except for surfaces with the root-mean-square (rms) roughness below ≈ 1 μm, where we observed lifetimes much longer than predicted by the theory. We show that this is due to out-diffusion of plasticizer from the soft PVC, which block the critical constrictions along the air flow channels. In water, some deviation between theory and experiments is observed which may be due to capillary forces. We discuss the role of cavitation for the failure time of suction cups in water.

When quickly detaching an elastomer from a counterface, viscoelasticity dramatically increases the perceived adhesion relative to its adiabatic or equilibrium value. Here, we report simulations on the sticking contact between a rigid cylinder and a viscoelastic half space revealing a maximum in the work of separation at intermediate pull-off velocities. Maximum tensile forces yet increase monotonically with the pull-off speed and the crack tip speed in accordance with the Persson-Brener approach. As predicted theoretically, the fracture mode transitions from interfacial crack propagation to quasi-uniform bond breaking with increasing range of adhesion.

We review a theory of crack propagation in viscoelastic solids. We consider both cracks in infinite systems and in finite-sized systems. As applications of the theory we consider two adhesion problems, namely pressure sensitive adhesives and the ball-flat adhesion problem. We also study crack propagation in the pig skin dermis, which is of medical relevance, and rubber wear in the context of tires.

We study the influence of rubber transfer films on the sliding friction between rectangular rubber blocks and a concrete surface. We present experimental results for the friction coefficient for a rubber compound sliding on a concrete surface contaminated by another rubber compound, for two different pairs (A, B) and (C, D) of rubber compounds. For the same rubber compounds, we present theory results which illustrate the relative importance of the viscoelastic and adhesive contribution to the sliding friction. We correlate the calculated rubber friction with the nature of the observed transfer films (or wear processes). Graphical Abstract

The adhesion paradox refers to the observation that for most solid objects no adhesion can be detected when they are separated from a state of molecular contact. The adhesion paradox results from surface roughness, and we present experimental and theoretical results that show that adhesion in most cases is "killed" by the longest-wavelength roughness. In addition, adhesion experiments between a human finger and a clean glass plate were carried out, and for a dry finger no macroscopic adhesion occurred. We suggest that the observed decrease in the contact area with increasing shear force results from nonadhesive finger-glass contact mechanics, involving large deformations of complex layered material.

Metallic seals are crucial machine elements in many important applications, e.g., in ultrahigh vacuum systems. Due to the high elastic modulus of metals, and the surface roughness which exists on all solid surfaces, if no plastic deformation would occur one expects in most cases large fluid flow channels between the contacting metallic bodies, and large fluid leakage. However, in most applications plastic deformation occurs, at least at the asperity level, which allows the surfaces to approach each other to such an extent that fluid leakage often can be neglected. In this study, we present an experimental set-up for studying the fluid leakage in metallic seals. We study the water leakage between a steel sphere and a steel body (seat) with a conical surface. The experimental results are found to be in good quantitative agreement with a (fitting-parameter-free) theoretical model. The theory predicts that the plastic deformations reduce the leak-rate by a factor $\approx 8$, 10 pages, 10 figures

We study the nominal (ensemble averaged) contact pressure $p(x)$ acting on a cylinder squeezed in contact with an elastic half-space with random surface roughness. The contact pressure is Hertzian-like for $\alpha < 0.01$ and Gaussian-like for $\alpha > 10$, where the dimensionless parameter $\alpha = h_{\rm rms}/\delta$ is the ratio between the root-mean-square roughness amplitude and the penetration for the smooth surfaces case (Hertz contact)., Comment: 6 pages, 5 figures. arXiv admin note: text overlap with arXiv:2007.13576

We study the role of electronegativity in sliding friction for five different two dimensional (2D) monolayer systems using density functional theory (DFT) with van der Waals (vdW) corrections. We show that the friction between the commensurate 2D layered systems depends strongly on the electronegativity difference of the involved atoms. All the 2D layered structures exhibit almost the same magnitude of friction force when sliding along the nonpolar path, independent of the material and the surface structures. In contrast, for sliding friction along the polar path, the friction force obeys a universal linear scaling law as a function of the electronegativity difference of its constituent atoms. Further analyses demonstrate that atomic dipoles in the 2D monolayers induced by the electronegativity difference enhance the corrugation of charge distribution and increase the sliding barrier accordingly. Our studies reveal that electronegativity plays an important role in friction of low dimensional systems, and will provide a strategy for designing nanoscale devices further., manuscript 13 pages, 5 figures. Supporting Information 1 table and 1 figure

I discuss fluid flow at the interface between solids with anisotropic roughness. I show that for randomly rough surfaces with anisotropic roughness, the contact area percolate at the same relative contact area as for isotropic roughness, and that the Bruggeman effective medium theory and the critical junction theory give nearly the same results for the fluid flow conductivity. This shows that, in most cases, the surface roughness observed at high magnification is irrelevant for fluid flow problems such as the leakage of static seals, and fluid squeeze-out., Comment: 14 pages, 7 figures

We study a simple model of a conveyor belt. We calculate the relation between the torque M and the belt–pulley slip s. We present numerical results for the M(s) relation, and for the frictional energy dissipation as a function of the slip, which is important for the rubber wear. The theory includes both the belt compliance and the pulley tread block stiffness. The theory shows that to minimize the friction and the related rubber wear, the pulley–belt system should be operated not at the slip where the torque is maximal, but at a lower slip. Thus, the belt–pulley system should be slightly “oversized” for the best performance.

Using molecular dynamics (MD) we study the dependency of the contact mechanics on the sliding speed when an elastically soft slab (block) is sliding on a rigid substrate with a ${\rm sin} (q_0 x)$ surface height profile. The atoms on the block interact with the substrate atoms by Lennard-Jones potentials. We consider contacts with and without adhesion. We found that the contact area and the friction force are nearly velocity independent for small velocities ($v < 0.25 \ {\rm m/s}$) in spite of the fact that the shear stress in the contact area is rather non-uniform. For the case of no adhesion the friction coefficient is very small. For the case of adhesion the friction coefficient is higher, and is mainly due to energy dissipation at the opening crack tip, where rapid atomic snap-off events occur during sliding. Adhesion experiments between a human finger and a clean glass plate were carried out, and for a dry finger no macroscopic adhesion occurred. We suggest that the observed decrease in the contact area with increasing shear force results from non-adhesive finger-glass contact mechanics, involving large deformations of a complex layered material., 14 pages, 20 Figures

We present experimental and theoretical results for the surface topography of a plastically deformed metallic (aluminum) block. When a hard spherical body (here a steel-, silica glass- or silicon nitride ball) with a smooth surface is indented in a metal block with a nominally flat, but still rough, surface, a spherical-cup-like indentation result due to plastic flow. The surface roughness in the indented region is, however, not entirely flattened. The long wavelength (macroasperity) content of the roughness result from the roughness on the original (aluminum) surface, but now plastically deformed. The roughness at short length scale, in the plastically deformed macroasperity contact regions, result from the roughness on the hard ball, and from inhomogeneous plastic flow. We model the contact mechanics using the boundary element method, combined with a simple numerical procedure to take into account the plastic flow. The theory can semi-quantitatively describe the modification of the roughness by the plastic flow. Since the fluid leakage of metallic seals in most cases is determined by the long wavelength roughness, we predict that the leakage can be estimated based on the elastoplastic contact mechanics model employed here. The plastic deformations of surfaces of some glassy polymers is very different from what we observed for aluminum, which we attribute to strong work-hardening and to inhomogeneous plastic flow for the polymers. Thus the numerical procedure to account for the plastic flow proposed here cannot be applied to glassy polymers in general., Comment: 10 pages, 18 figures

We calculate heat transfer between a 2D sheet (e.g. graphene) and a dielectric in presence of a gate voltage. The gate potential induces surface charge densities on the sheet and dielectric, which results in electric field, which is coupled to the surface displacements and, as a consequence, resulting an additional contributions to the radiative heat transfer. The electrostatic and van der Waals interactions between the surface displacement result in the phonon heat transfer, which we calculate taking into account the nonlocality of these interactions. Numerical calculations are presented for heat transfer between graphene and a SiO$_2$ substrate., 10 pages, 2 figures

We have developed a theory of air leakage at interfaces between two elastic solids with application to suction cups in contact with randomly rough surfaces. We present an equation for the airflow in narrow constrictions which interpolates between the diffusive and ballistic (Knudsen) air-flow limits. To test the theory, we performed experiments using two different suction cups, made from soft polyvinylchloride (PVC), in contact with sandblasted polymethylmethacrylate (PMMA) plates. We found that the measured time to detach (lifetime) of the suction cups was in good agreement with theory, except for surfaces with a root-mean-square (rms) roughness below ≈1 μm, where diffusion of plasticizer from the PVC to the PMMA surface caused blockage of critical constrictions. The suction cup volume, stiffness, and elastic modulus have a huge influence on the air leakage and hence the failure time of the cups. Based on our research we propose an improved biomimetic design of suction cups that could show improved failure times with varying degrees of roughness under dry and wet environments.

When an elastic block is squeezed in contact with a substrate the contact will in general consist of many asperity contact regions. During sliding the long-range elastic coupling between the contact regions have a big influence on the sliding dynamics: when the loading force increases the density of contact regions increases, which affects the lateral coupling between the contact region, and introduces a dependence of the friction force on the loading force. Here we present a full three-dimensional model study of the role of the elastic coupling on the friction force. The theory is applied to rubber friction, but the mechanism for the dependence of the friction coefficient on the load is relevant for non-rubber materials as well.

We study adhesion and friction between smooth glass, and fresh and aged Styrene Butadiene – Isoprene rubber blend (SBR-IR). The friction and adhesion are only slightly modified by the aging process, but elongation at break, and rubber toughness, are strongly reduced. We attribute this to changes in the crosslink density, a decrease in the filler matrix strength, and to the formation and growth of crack-like defects. The latter have a small influence on adhesion and friction, but a large effect on the elongation at break.

Interfacial leakage of air in hydrogenated nitrile butadiene rubber (HNBR) O-ring seals exposed to sub-ambient temperatures is studied. Flange-type fixtures with sealing surfaces produced by 3 different surface finish processes are used. When the seals are cooled down to temperatures below the elastomer glass transition point T g of (−23 °C), an abrupt increase of air leakage ( > 10 − 2 cm 3 / min ) is observed. The effects of surface finish conditions, compression ratio, grease lubrication and additions of carbon black in the HNBR on the cold leakage are discussed. Persson's contact mechanics and effective medium leakage theory coupled with finite element analysis (FEA) of the HNBR seals are utilized to capture the changes in the contact area and pressure with cooling and predict the seal failure temperatures. The main cause for the cold seal failures is believed to be the detachment of the elastomer seals from their mating sealing parts due to the elastomer thermal contraction and the negligible recovery of the HNBR in cold environment. In addition, the adhesive rubber-substrate interface influences the detachment and seal failure.

Adhesion between a glass ball and a polydimethylsiloxane (PDMS) sample is dependent on the PDMS cross-link density, and the transformation of the material from the uncrosslinked liquid state to the fully crosslinked solid state is investigated in this study. The physical picture reflected a gradual transition from capillary forces driven contact mechanics to the classical Johnson-Kendall-Roberts (JKR)-type contact mechanics. PDMS was produced by mixing the base fluid and a cross-linker at a ratio of 10 : 1 and allowed to slowly cross-link at room temperature with simultaneous measurement of the ball-PDMS interaction force. The PDMS sample was in the liquid state during the first ≈16 hours, and in this case the ball-PDMS interaction was purely adhesive, i.e., no repulsive interaction was observed. Later at the PDMS gel-point the cross-linked PDMS clusters percolate, converting the fluid into a soft (fluid-filled) poroelastic solid. In the transition period, PDMS appears similar to pressure-sensitive adhesives. There we observe so-called "stringing" and permanent deformation of the material impacted by the ball. At room temperature, it takes more than ∼100 hours for PDMS to fully cross-link that can be confirmed by the comparison with the earlier-studied reference PDMS produced at elevated temperatures.

We present a general theory of electroadhesion assuming layered materials with finite electric conductivity and an air gap resulting from interfacial surface roughness. The theory reduces to the results derived in Persson (2018 J. Chem. Phys. 148 144701) in the appropriate limits. We present numerical results to illustrate the theory.

We study a simple contact mechanics model of the vertebrate cartilage, which includes (bulk) osmotic effects. The surface roughness power spectrum of a pig cartilage is obtained from the measured surface topography. Using the Reynolds equations with fluid flow factors, calculated using the Persson contact mechanics theory and the Bruggeman effective medium theory, we show how the area of contact and the average interfacial separation change with time. We found that in most cases the contact area percolates, resulting in islands of confined fluid which carry most of the external load. Most importantly, we find that the pressure in the area of real contact is nearly independent of the external load, and well below 1 MPa. This allows the surfaces in the area of "real contact", to be separated (at nanometer range separation distance) by osmotic repulsion, resulting in a very small (breakloose) friction force observed even after a long time of stationary contact.

Rubber friction depends on the surface roughness of the counter surface, e.g. a road surface. We have measured the friction for two rubber compounds sliding on randomly rough surfaces produced by 3D-printing. The surfaces had different macro-roughness and the friction experiments were performed over six decades in speeds, from 10−6 m s−1 to 1 m s−1, on both dry and lubricated substrates. The viscoelastic modulus master curves of the rubber compounds, and their large-strain effective modulus were obtained from dynamic mechanical analysis (DMA). The measured friction coefficients were compared to the calculations of rubber friction using Persson's contact mechanics theory. The role of the macro-level roughness is discussed.

We present experimental results for the elastic and plastic deformation of sandblasted polymer balls resulting from contacts with flat smooth steel and silica glass surfaces. Nearly symmetric, Gaussian-like height probability distributions were observed experimentally before and remarkably, also after the polymer balls were deformed plastically. For all the polymers studied we find that the surface roughness power spectra for large wavenumbers (short length scales) are nearly unchanged after squeezing the polymer balls against flat surfaces. We attribute this to non-uniform plastic flow processes at the micrometer length scale. The experimental data are analyzed using the Persson contact mechanics theory with plasticity and with finite-element method (FEM) calculations.

Seals are crucial machine elements, for example in hydraulic cylinders. However, especially in regard to dynamic seals, the theoretical understanding of the sealing mechanism is still insufficient. A physically motivated simulation can help to gain a more detailed understanding. In this contribution a elastohydrodynamic (EHD) seal simulation is presented. It is directly implemented in the commercial Software ABAQUS. The fluid film is considered by implementing the Reynolds equation. For a physically motivated simulation Persson’s theory of contact mechanics and rubber friction is used to calculate the solid contribution to the total friction of a hydraulic seal. Simulations for an oscillating motion of a cylinder rod, sealed by an O-ring seal, are carried out for different velocities and pressures. A qualitative comparison between measurement and simulation is provided. Hysteresis effects and the contributions from both, adhesive and viscoelastic friction to the total solid friction are investigated. The physical origin of these effects is discussed in order to provide a detailed understanding of the dynamic sealing mechanism.

The frictional anisotropy of metallic nanoparticles is investigated using a molecular dynamics method. Calculations of anisotropy have been performed for aluminum, palladium, and platinum nanoparticles containing 10,000 atoms. Anisotropy is studied at high sliding velocities of nanoparticles over the graphene surface. The influences of incommensurability and short-range order of nanoparticles’ contact surfaces lead to the absence of pronounced angular dependence of frictional force.

The research of temperature properties and correlation of friction force of metallic nanoparticles on graphene is represented. Modeling was led by molecular dynamics method through CUDA-technology. Calculations have been performed for aluminum, palladium, cobalt and platinum nanoclusters containing from 10000 to 20000 atoms at the temperatures from 300 K to 1400 K. Radial distribution function is built to analyze the structural changes of nanoparticles. We discuss the strong influence of the types of metals on the form of functions describing the behavior of nanoparticles during motion.

Abstract. We derive approximate mean field equations for the fluid flow between elastic solids with randomly rough surfaces including interfacial fluid slip and shear thinning. We present numerical results for the fluid flow and friction factors for realistic systems, in particular, we consider the case of an elastic cylinder with random surface roughness in relative sliding contact with a flat rigid (low-energy) counter-surface. We present experimental data for the sliding friction between rubber stoppers and glass barrels lubricated with baked-on silicone oil. We find that the frictional shear stress acting in the rubber asperity contact regions is nearly velocity independent for velocities in the 10-1000μm/s range, and very small $ \tau_{{\rm f}} \approx 0.04$τf≈0.04 MPa, while for bare glass in silicone oil $ \tau_{{\rm f}}$τf is much larger and velocity dependent. Graphical abstract

Seals are crucial machine elements in hydraulic devices. However, especially with regard to dynamic seals – for example in cylinder applications – the physical understanding of the sealing mechanism is still insufficient. In this paper a physically based, transient elastohydrodynamic simulation for translational hydraulic seals is presented. The deformation of the seal is calculated in a dynamic finite element (FE) simulation, hyper- and viscoelastic material properties are taken into account. For the numerical calculation of the fluid film and its influences on the seal deformation the FE simulation is coupled with an implementation of the transient Reynold’s equation. For a physically based calculation of the solid contact, the FE-model is coupled with Persson’s theory of rubber friction and contact mechanics. Both, normal force and solid friction are implemented. In a simulation study the influence of the relative velocity in the contact between the elastic, highly deformable seal and a hard cylinder is investigated. The initial phase of motion is investigated in detail. The simulation results are compared to experimental data of a lubricated sliding contact between an nitrile butadiene rubber (NBR) O-ring and a rough steel surface.

International audience; There is a growing interest on touchscreens displaying tactile feedback due to their tremendous potential in consumer electronics. In these systems, the friction between user's fingerpad and the surface of touchscreen is modulated to display tactile effects. One of the promising techniques used in this regard is electrostatic actuation. If, for example, an alternating voltage is applied to the conductive layer of a surface capacitive touchscreen, an attractive electrostatic force is generated between finger and the surface which results in an increase in frictional forces acting on the finger moving on the surface. By altering the amplitude, frequency, and the waveform of this signal, a rich set of tactile effects can be generated on the touchscreen. Despite the ease of implementation and its powerful effect on our tactile sensation, the contact mechanics leading to an increase in friction due to electroadhesion has not been fully understood yet. In this paper, we present experimental results for how the friction between a finger and a touchscreen depends on the electrostatic attraction and the applied normal pressure. The dependency of the finger-touchscreen interaction on the applied voltage, and on several other parameters, is also investigated using a mean field theory based on multiscale contact mechanics. We present detailed theoretical analysis of how the area of real contact and the friction force depend on contact parameters, and show that it is possible to further augment the friction force, and hence the tactile feedback displayed to the user by carefully choosing those parameters.

Soft adhesive pads are needed for many robotics applications, and one approach is based on electroadhesion. Here we present a general analytic model and numerical results for electroadhesion for soft solids with an arbitrary time-dependent applied voltage, and an arbitrary dielectric response of the solids, and including surface roughness. We consider the simplest coplanar-plate-capacitor model with a periodic array of conducting strips located close to the surface of the adhesive pad, and discuss the optimum geometrical arrangement to obtain the maximal electroadhesion force. For surfaces with roughness the (non-contact) gap between the solids will strongly influence the electroadhesion, and we show how the electroadhesion force can be calculated using a contact mechanics theory for elastic solids. The theory and models we present can be used to optimize the design of adhesive pads for robotics application.

We study the linear and nonlinear viscoelastic properties of two tire tread compounds. We discuss the difference in nonlinear response between the oscillatory tensile and shear modes. We also analyze strain relaxation (creep) data for the same systems. We discuss what type of measurements are most suitable for obtaining the viscoelastic modulus used in rubber friction calculations.

Using molecular dynamics we study the dependence of the friction force on the sliding speed when an elastic slab (block) is sliding on a rigid substrate with a surface height profile. The friction force is nearly velocity independent due to phonon emission at the closing and opening crack tips, where rapid atomic snap-in and -out events occur during sliding. The rapid events result from lattice trapping and are closely related to the velocity gap and hysteresis effects observed in model studies of crack propagation in solids. This indicates that the friction force is dominated by processes occurring at the edges of the contact area, which is confirmed by calculations showing that the friction force is independent of the normal force. The friction force increases drastically when the sliding velocity approaches the solid transverse sound velocity, as expected from the theory of cracks.

Silicone rubber is often used to obtain replica of surfaces which are hard to study directly. Here we discuss under what conditions engineering stylus measurements can be used to obtain the correct surface roughness from the replica. We also show how thin vertical slices of the silicone rubber can be used to obtain the surface roughness power spectra for the long-wavelength roughness on even very rough surfaces, such as road surfaces, which may be hard to probe directly with standard optical or stylus instruments.

In this work, we discuss important improvements of asperity models. Specifically, we assess the predictive capabilities of a recently developed multiasperity model, which differs from the original Greenwood and Williamson model by (i) including the coupling between the elastic fields generated by each contact spot, and (ii) taking into account the coalescence among the contact areas, occurring during the loading process. Interaction of the elastic field is captured by summing the contributions, which are analytically known, of the elastic displacements in a given point of the surface due to each Hertzian-like contact spot. The coalescence is instead considered by defining an equivalent contact spot in such a way to guarantee conservation of contact area during coalescence. To evaluate the accuracy of the model, a comparison with fully numerical ‘exact’ calculations and Persson’s contact mechanics theory of elastic rough surfaces is proposed. Results in terms of contact area versus load and separation versus load show that the three approaches give almost the same predictions, while traditional asperity models neglecting coalescence and elastic coupling between contact regions are unable to correctly capture the contact behavior. Finally, very good results are also obtained when dealing with the probability distribution of interfacial stresses and gaps.

Machine elements and mechanical components have often surfaces with anisotropic roughness, which may result from the machining processes, e.g. grinding, or from wear. Hence, it is important to understand how surface roughness anisotropy affects the contact mechanics properties, such as friction and the interface separation, which is important for lubricated contacts. Here we extend a multiscale mean-field model to the lubricated contact between a soft (e.g. rubber) elastic solid and a rigid countersurface. We consider surfaces with anisotropic surface roughness, and discuss how the fluid flow factors and friction factors depend on the roughness power spectral density, as well as on the location of roughness on the interacting solids. Finally, we present an experimental study of the lubricated sliding contact between a nitrile butadiene rubber O-ring and steel surfaces with different kinds of isotropic and anisotropic surface roughness. The good quantitative comparison between the experimental results and the theory predictions suggests that the multiscale lubrication mechanisms are accurately captured by the theory.

There are two contributions to the friction force when a rubber block is sliding on a hard and rough substrate surface, namely, a contribution Fad = τf A from the area of real contact A and a viscoelastic contribution Fvisc from the pulsating forces exerted by the substrate asperities on the rubber block. Here we present experimental results obtained at different sliding speeds and temperatures, and we show that the temperature dependency of the shear stress τf, for temperatures above the rubber glass transition temperature Tg, is weaker than that of the bulk viscoelastic modulus. The physical origin of τf for T > Tg is discussed, and we propose that its temperature dependency is determined by the rubber molecule segment mobility at the sliding interface, which is higher than in the bulk because of increased free-volume effect due to the short-wavelength surface roughness. This is consistent with the often observed reduction in the glass transition temperature in nanometer-thick surface layers of glassy polymers. For temperatures T < Tg, the shear stress τf is nearly velocity independent and of similar magnitude as observed for glassy polymers such as PMMA or polyethylene. In this case, the rubber undergoes plastic deformations in the asperity contact regions and the contact area is determined by the rubber penetration hardness. For this case, we propose that the frictional shear stress is due to slip at the interface between the rubber and a transfer film adsorbed on the concrete surface. Locked until 12.6.2019 due to copyright restrictions.Published by AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Chemical Physics and may be found at https://doi.org/10.1063/1.5037136

The understanding and control of human skin contact against technological substrates is the key aspect behind the design of several electromechanical devices. Among these, surface haptic displays that modulate the friction between the human finger and touch surface are emerging as user interfaces. One such modulation can be achieved by applying an alternating voltage to the conducting layer of a capacitive touchscreen to control electroadhesion between its surface and the finger pad. However, the nature of the contact interactions between the fingertip and the touchscreen under electroadhesion and the effects of confined material properties, such as layering and inelastic deformation of the stratum corneum, on the friction force are not completely understood yet. Here, we use a mean field theory based on multiscale contact mechanics to investigate the effect of electroadhesion on sliding friction and the dependency of the finger-touchscreen interaction on the applied voltage and other physical parameters. We present experimental results on how the friction between a finger and a touchscreen depends on the electrostatic attraction between them. The proposed model is successfully validated against full-scale (but computationally demanding) contact mechanics simulations and the experimental data. Our study shows that electroadhesion causes an increase in the real contact area at the microscopic level, leading to an increase in the electrovibrating tangential frictional force. We find that it should be possible to further augment the friction force, and thus the human tactile sensing, by using a thinner insulating film on the touchscreen than used in current devices.

We discuss the origin of the low friction observed for some elastically soft materials, such as hydrogels and the human cartilage. When a soft elastic solid is squeezed against another solid in a fluid, if the nominal contact pressure is high enough, after long enough contact time the contact area percolates, resulting in islands of confined fluid. For charged surfaces, with charges of equal sign, the osmotic pressure in the area of “real contact” may be large enough to keep the surfaces separated at nanometer separation. In this case the solid contact pressure (here the osmotic pressure) in the area of “real contact” will be nearly independent of the external load. The finite surface separation in the area of “real contact” results in a very small (breakloose) friction force even after long time of stationary contact.

We study the adhesion between differently processed glass and filled bromobutyl rubber in dry conditions, in water, and in silicone oil. The boundary line between contact and non-contact in adhesion experiments can be considered as a mode I crack, and we show that viscoelastic energy dissipation, close to the opening (or closing) crack tip and surface roughness, strongly affects the work of adhesion. We observe strong adhesion hysteresis and, in contrast to the Johnson–Kendall–Roberts theory prediction for elastic solids, this results in a pull-off force (and work of adhesion) which depends on the loading force and contact time. In particular, for the system immersed in water and silicone oil, we register very weak adhesive bonding. For glass ball with baked-on silicone oil, the pull-off force is nearly independent of the contact time, but this is not observed for the unprocessed glass surface. This is the authors’ accepted and refereed manuscript to the article. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in The Journal of Chemical Physics and may be found at https://aip.scitation.org/doi/10.1063/1.5025605.