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The complex physics behind electroadhesion-based tactile displays poses an enormous modeling challenge since not only the fingerpad structure with multiple nonlinear layers, but also the roughness at the microscopic scale play a decisive role. To investigate tactile perception, a potential model should also offer the possibility to extract mechanical stimuli at the sites of the relevant mechanoreceptors. In this paper, we present a two-scale approach that involves a finite element model (FEM) at the macroscopic scale and a simple bearing area model (BAM) that accounts for the measured roughness on the papillary ridges. Both separate scales couple in an iterative way using the concept of an equivalent air gap. We show that the electroadhesion-induced changes in friction and contact area predicted by the proposed model are in qualitative agreement with recent experimental studies. In a simple example, we demonstrate that the model can readily be extended by a neural dynamics model to investigate the tactile perception of electroadhesion., 22 pages, 9 figures

The coefficient of friction due to bulk viscoelastic losses corresponding to multiscale roughness can be computed with Persson's theory. In the search for a more complete understanding of the parametric dependence of the friction coefficient, we show asymptotic results at low or large speed for a generalized Maxwell viscoelastic material, or for a material showing power law storage and loss factors at low frequencies. The ascending branch of friction coefficient at low speeds highly depends on the rms slope of the surface roughness (and hence on the large wave vector cutoff), and on the ratio of imaginary and absolute value of the modulus at the corresponding frequency, as noticed earlier by Popov. However, the precise multiplicative coefficient in this simplified equation depends in general on the form of the viscoelastic modulus. Vice versa, the descending (unstable) branch at high speed mainly on the amplitude of roughness, and this has apparently not been noticed before. Hence, for very broad spectrum of roughness, friction would remain high for quite few decades in sliding velocity. Unfortunately, friction coefficient does not depend on viscoelastic losses only, and moreover there are great uncertainties in the choice of the large wave vector cutoff, which affect friction coefficient by orders of magnitudes, so at present these theories do not have much predictive capability.

Adhesion and, its interplay with friction, is central in several engineering applications involving soft contacts. Recently, there has been an incredible push towards a better understanding on how the apparent contact area evolves when a shear load is applied to an adhesive soft contact, both experimentally and theoretically. Although soft materials are well-known to exhibit rate-dependent properties, there is still a lack of understanding in how the loading rate could affect the contact area shrinking. Indeed, most of the experiments involving a sphere-flat contact have been conducted at a fixed loading rate, and, so far, analytical models have assumed a constant work of adhesion, independent on the peeling velocity. Here, by using linear elastic fracture mechanics, an analytical model is derived for the contact of a rigid sphere on a soft adhesive substrate, which is aimed at elucidating the effect that a rate-dependent work of adhesion has on the contact area shrinking. The model results show that contact area reduction is very sensitive to the loading rate, with slower loading rates promoting a stronger shrinking, which seems in agreement with Literature results. Furthermore it is shown that rate effects enhance the apparent interfacial toughness, i.e. more energy is needed to drive the system from full stick up to gross sliding.

Recently, Dalvi and co-authors have shown detailed experimental data of adhesion of soft spheres with rough substrates with roughness measured down to almost the atomic scale, finding that the Persson and Tosatti theory gave satisfactory predictions of the apparent work of adhesion during loading, once the increase of the surface area due to roughness is correctly computed at extremely small scales. We show that unloading data would show similar correlation with the Persson–Tosatti’s simple criterion, but for a much larger effective work of adhesion, which therefore becomes not an “intrinsic” property. This suggests either strong hysteresis even at apparently very low peeling velocities or the need to use a criterion that has different behavior during loading and unloading. We attempt this inspired by the results of Guduru for a simple case of axisymmetric waviness, and a much better fit of the experimental data by Dalvi and co-authors is obtained using the entire set of data at loading and unloading, even assuming a single work of adhesion value. However, we cannot rule out that both (viscoelastic) and (roughness-induced) enhancement effects coexist in these data.

Mode-coupling instabilities are known to trigger self-excited vibrations in sliding contacts. Here, the conditions for mode-coupling (or “flutter”) instability in the contact between a spherical oscillator and a moving viscoelastic substrate are studied. The work extends the classical 2-Degrees-Of-Freedom conveyor belt model and accounts for viscoelastic dissipation in the substrate, adhesive friction at the interface and nonlinear normal contact stiffness as derived from numerical simulations based on a boundary element method capable of accounting for linear viscoelastic effects. The linear stability boundaries are analytically estimated in the limits of very low and very high substrate velocity, while in the intermediate range of velocity the eigenvalue problem is solved numerically. It is shown how the system stability depends on externally imposed parameters, such as the substrate velocity and the normal load applied, and on contact parameters such as the interfacial shear strength $$\tau _{0}$$ τ 0 and the viscoelastic friction coefficient. In particular, for a given substrate velocity, there exist a critical shear strength $$\tau _{0,crit}$$ τ 0 , c r i t and normal load $$F_{n,crit}$$ F n , c r i t , which trigger mode-coupling instability: for shear stresses larger than $$\tau _{0,crit}$$ τ 0 , c r i t or normal load smaller than $$F_{n,crit}$$ F n , c r i t , self-excited vibrations have to be expected.

Experimental results on nonlinear vibration localization in a cyclic chain of weakly coupled oscillators with clearance nonlinearity are reported. Numerical modelling and analysis complements the experimental study. A reduced order model is derived and numerical analysis based on the harmonic balance method demonstrates the existence of multiple classes of stable spatially localized nonlinear vibration states. The experiments agree very well with the numerical results. The findings suggest that vibration localization due to fundamentally nonlinear effects may also arise in mechanical structures with relevance in engineering.

We derive a very simple and effective stickiness criterion for solids having random roughness using a new asymptotic theory, which we validate with that of Persson and Scaraggi and independent numerical experiments. Previous claims that stickiness may depend on small scale quantities such as rms slopes and/or curvatures, obtained by making oversimplified assumptions on the contact area geometry, are largely incorrect, as the truncation of the PSD spectrum of roughness at short wavelengths is irrelevant. We find stickiness is destroyed typically at roughness amplitudes up to three orders of magnitude larger than the range of attractive forces. With typical nanometer values of the latter, the criterion gives justification to the qualitative well known empirical Dalhquist criterion for stickiness which demands adhesives to have elastic modulus lower than about 1MPa. The results clarifies a much debated question in both the scientific and technological world of adhesion, and may serve as benchmark for better comprehension of the role of roughness.

Unstable friction-induced vibrations are considered an annoying problem in several fields of engineering. Although several theoretical analyses have suggested that friction-excited dynamical systems may experience sub-critical bifurcations, and show multiple coexisting stable solutions, these phenomena need to be proved experimentally and on continuous systems. The present work aims to partially fill this gap. The dynamical response of a continuous system subjected to frictional excitation is investigated. The frictional system is constituted of a 3D printed oscillator, obtained by additive manufacturing that slides against a disc rotating at a prescribed velocity. Both a finite element model and an experimental setup has been developed. It is shown both numerically and experimentally that in a certain range of the imposed sliding velocity the oscillator has two stable states, i.e. steady sliding and stick–slip oscillations. Furthermore, it is possible to jump from one state to the other by introducing an external perturbation. A parametric analysis is also presented, with respect to the main parameters influencing the nonlinear dynamic response, to determine the interval of sliding velocity where the oscillator presents the two stable solutions, i.e. steady sliding and stick–slip limit cycle.

Electroadhesion is a very hot topic in tribology due to its implications for the science of surface haptics. Building on theories of Persson, we develop a simpler theory for electroadhesion between rough surfaces using the bearing area model of Ciavarella. The theory is derived for the cases of conducting and insulating bodies and shows that pull-off forces depend mostly on the applied voltage, the surface root mean square (RMS) height, and the longest wavelength in the surface representation. However, the real contact area and friction additionally depend on rms slopes and hence on truncation of the roughness spectrum. Two stickiness criteria are derived based on the present theory and on the energy balance proposed by Persson and Tosatti. The coefficient of friction decays with the normal pressure, tending to a plateau in a manner consistent with existing experiments. Italian Ministry of Education, University and Research Deutsche Forschungsgemeinschaft (DFG)

As often done in design practice, the Wöhler curve of a specimen, in the absence of more direct information, can be crudely retrieved by interpolating with a power-law curve between static strength at a given conventional low number of cycles N0 (of the order of 10-103), and the fatigue limit at a “infinite life”, also conventional, typically N∞=2·106 or N∞=107 cycles. These assumptions introduce some uncertainty, but otherwise both the static regime and the infinite life are relatively well known. Specifically, by elaborating on recent unified treatments of notch and crack effects on infinite life, and using similar concepts to the static failure cases, an interpolation procedure is suggested for the finite life region. Considering two ratios, i.e. toughness to fatigue threshold FK=KIc/DKth, and static strength to endurance limit, FR =sR /Ds0, qualitative trends are obtained for the finite life region. Paris’ and Wöhler’s coefficients fundamentally depend on these two ratios, which can be also defined “sensitivities” of materials to fatigue when cracked and uncracked, respectively: higher sensitivity means stringent need for design for fatigue. A generalized Wöhler coefficient, k’, is found as a function of the intrinsic Wöhler coefficient k of the material and the size of the crack or notch. We find that for a notched structure, k

Adhesive contact of the Hertzian indenter with an incompressible elastic substrate bi-directionally stretched along the indenter principal planes of curvature is considered in the Johnson–Kendall–Roberts theoretical framework. An approximate model is constructed by examining energy release rate conditions only on the edges of the minor and major axes of the contact ellipse. The effect of weak coupling between fracture modes I and II is introduced using a phenomenological mode-mixity function. This study was motivated by the need to model a passive–adhesive mechanism in cell mechanics on stretchable substrates.

There is ample evidence of ThermoElastic Instabilities (TEI) occurring in sliding contacts. The very first experiments of JR Barber in 1969 suggested wear interacts in the process of localization of contact into “hot spots”. However, studies on the interaction of TEI with wear are scarce. We consider the case of two sliding halfspaces and make a perturbation analysis permitting the formation of waves migrating over the two bodies, in presence of wear. We find that for exactly identical bodies wear does not affect the stability boundary. In the other limit case of bad conductor against a good conductor, wear tends to suppress TEI completely. Intermediate cases show a complex range of possible effects: for certain thermomechanical properties wear may even reduce the critical speed.

Rubber friction plays a fundamental role in the study of the tire-road interaction and still represents a topic of discussion for both academics and manufacturing companies, especially with the introduction of the concept of multiscale roughness [1, 2]. Taking into account that the road surface is a hard substrate, the two contributions to rubber friction can be considered to be (i) hysteretic phenomena deriving from time dependent viscoelastic deformations of the rubber due to the substrate asperities and (ii) adhesive effects. From the modelling point of view, the estimation of each contribution represents a great challenge, and both formulations are inevitably affected by the presence of empirical constants. For example, hysteretic friction could be in principle computed by a full multiscale Persson’s theory [1, 3], but the latter one ultimately embraces an arbitrary choice of the cutoff frequency value, and, furthermore, the full multiscale theory can be in most cases simplified [4]. The adhesive contribution, instead, remains fundamentally empirically described by fitting functions and parameters, and, despite considerable progress and huge effort in this research field, it continues to represent the greatest challenge as well as to recognize the relative importance of the two contributions [5]. In this work, an analysis of the results obtained with the different formulations available in literature is proposed with particular reference to the empirical constants variability.

The interaction between contact area and frictional forces in adhesive soft contacts is receiving much attention in the scientific community due to its implications in many areas of engineering such as surface haptics and bioinspired adhesives. In this work, we consider a soft adhesive sphere that is pressed against a rigid substrate and is sheared by a tangential force where the loads are transferred to the sphere through a normal and a tangential spring, representing the loading apparatus stiffness. We derive a general linear elastic fracture mechanics solution, taking into account also the interaction between modes, by adopting a simple but effective mixed-mode model that has been recently validated against experimental results in similar problems. We discuss how the spring stiffness affects the stability of the equilibrium contact solution, i.e. the transition to separation or to sliding.

Frictional interfaces exhibits a very rich dynamical behavior due to frictional interactions. This work focuses on the transition between spatially localized and propagating stick-slip motion. To overcome the difficulties related to the non-smoothness of the friction law we have studied two models: (model I) a friction-excited chain of weakly coupled oscillators excited by a frictional moving belt and (model II) a chain of Van der Pol oscillators. The two models show very similar dynamical features. Both exhibit discrete breathers (i.e. spatially localized periodic solutions) solutions for low coupling and show propagation along the chain of high amplitude limit cycles for stronger elastic coupling between the unit cells. In both models the transition from discrete breathers to propagating limit cycles happens through a nucleation process and, above a certain critical coupling, the velocity of propagation scales linearly with the elastic coupling coefficient. We suggest that dynamical features similar to what was demonstrated in this work are expected for models that are different quantitatively but preserve the same single-unit topology.

International audience; Many engineering structures are composed of weakly coupled sectors assembled in a cyclic and ideally symmetric configuration, which can be simplified as forced Duffing oscillators. In this paper, we study the emergence of localized states in the weakly nonlinear regime. We show that multiple spatially localized solutions may exist, and the resulting bifurcation diagram strongly resembles the snaking pattern observed in a variety of fields in physics, such as optics and fluid dynamics. Moreover, in the transition from the linear to the nonlinear behaviour isolated branches of solutions are identified. Localization is caused by the hardening effect introduced by the nonlinear stiffness, and occurs at large excitation levels. Contrary to the case of mistuning, the presented localization mechanism is triggered by the nonlinearities and arises in perfectly homogeneous systems.

International audience; This paper gives a theoretical analysis for the fundamental problem of anisotropy induced by shear forces onan adhesive contact, discussing the experimental data of the companion Letter. We present a fracture mechanicsmodel where two phenomenological mode-mixity functions are introduced to describe the weak couplingbetween modes I and II or I and III, which changes the effective toughness of the interface. The mode-mixityfunctions have been interpolated using the data of a single experiment and then used to predict the behavior of thewhole set of experimental observations. The model extends an idea by Johnson and Greenwood, to solve purelymode I problems of adhesion in the presence of a nonaxisymmetric Hertzian geometry, to the case of ellipticalcontacts sheared along their major or minor axis. Equality between the stress intensity factors and their criticalvalues is imposed solely at the major and minor axes. We successfully validate our model against experimentaldata. The model predicts that the punch geometry will affect both the shape and the overall decay of the shearedcontact area.

Since the early study by Grosch in 1963 it has been known that rubber friction shows generally two maxima with respect to speed&mdash, the first one attributed to adhesion, and another at higher velocities attributed to viscoelastic losses. The theory of Kl&uuml, ppel and Heinrich and that of Persson suggests that viscoelastic losses crucially depend on the &ldquo, multiscale&rdquo, aspect of roughness and in particular on truncation at fine scales. In this study, we comment a little on both theories, giving some examples using Persson&rsquo, s theory on the uncertainties involved in the truncation of the roughness spectrum. It is shown how different choices of Persson&rsquo, s model parameters, for example the high-frequency cutoff, equally fit experimental data on viscoelastic friction, hence it is unclear how to rigorously separate the adhesive and the viscoelastic contributions from experiments.

The anomalous propagation of short cracks shows generally exponential fatigue crack growth but the dependence on stress range at high stress levels is not compatible with Paris’ law with exponent m = 2 . Indeed, some authors have shown that the standard uncracked SN curve is obtained mostly from short crack propagation, assuming that the crack size a increases with the number of cycles N as da dN = H Δ σ h a where h is close to the exponent of the Basquin’s power law SN curve. We therefore propose a general equation for crack growth which for short cracks has the latter form, and for long cracks returns to the Paris’ law. We show generalized SN curves, generalized Kitagawa–Takahashi diagrams, and discuss the application to some experimental data. The problem of short cracks remains however controversial, as we discuss with reference to some examples.

There is no simple theory at present to predict accurately the decay of pull-off in the adhesion of randomly rough surfaces. The asperity model of Fuller and Tabor has shown significant error in recent numerical investigations by Pastewka and Robbins of self-affine random roughness from micrometer to atomic scale which corresponds to low values of Tabor parameter. For sinusoidal contact, the Johnson parameter, originally introduced for the JKR regime (from Johnson-Kendall-Roberts) is the dominant parameter ruling the pull-off at intermediate Tabor values. Hence, we define a generalized Johnson parameter as the ratio between the adhesive energy to the elastic strain energy to flatten the surface in the case of multiscale roughness and find that it correlates very well with the data of Pastewka and Robbins spanning almost five orders of magnitude of reduction from theoretical strength, improving significantly with respect to other possible single parameter criteria. For the most important case in practice, that of low fractal dimensions, this suggests the product of amplitude and slope of the largest wavelength components of roughness dominate pull-off decay, and not small scales features like slopes and curvatures, as suggested by Pastewka and Robbins.

There are two main approximate theories in the contact of rough solids: Greenwood-Williamson asperity theories (GW) and Persson theories. Neither of them has been fully assessed so far with respect to load-separation curves. Focusing on the most important case of low fractal dimension (D f = 2.2) with extensive numerical studies we find that: (i) Persson’s theory describes well the regime of intermediate pressures/contact area, but requires significant corrective factors: the latter depend also on upper wavevector cutoff of the roughness; hence, (ii) Persson’s theory does not predict the correct functional dependence on magnification; (iii) asperity theories in the discrete version even neglecting interaction effects are more appropriate in the range of relatively large separations, also to take into consideration of the large scatter in actual realization of the surface.

We study the adhesion of a surface with a ‘dimple’ which shows a mechanism for a bi-stable adhesive system in surfaces with spaced patterns of depressions, leading to adhesion enhancement, high dissipation and hysteresis. Recent studies were limited mainly to the very short range of adhesion (the so-called JKR regime), while we generalize the study to a Maugis cohesive model. A ‘generalized Tabor parameter’, given by the ratio of theoretical strength to elastic modulus, multiplied by the ratio of dimple width to depth has been found. It is shown that bistability disappears for generalized Tabor parameter less than about 2. Introduction of the theoretical strength is needed to have significant results when the system has gone in full contact, unless one postulates alternative limits to full contact, such as air entrapment, contaminants or fine scale roughness. Simple equations are obtained for the pull-off and for the full contact pressure in the entire set of the two governing dimensionless parameters. A qualitative comparison with results of recent experiments with nanopatterned bioinspired dry adhesives is attempted in light of the present model.

Snaking bifurcations in a chain of mechanical oscillators are studied. The individual oscillators are weakly nonlinear and subject to self-excitation and subcritical Hopf-bifurcations with some parameter ranges yielding bistability. When the oscillators are coupled to their neighbours, snaking bifurcations result, corresponding to localised vibration states. The snaking patterns do seem to be more complex than in previously studied continuous systems, comprising a plethora of isolated branches and also a large number of similar but not identical states, originating from the weak coupling of the phases of the individual oscillators.

Wedge-shaped frictional dampers are widely used in civil, mechanical and aeronautical engineering with the purpose to limit and damp vibrations, increase component fatigue life, or resist seismic loads. The wedge shape induces normal load variations which complicates the analysis. Here, we study a model which can be considered a generalization of the Griffin model, originally devised for underplatform dampers in turbine blade attachments. The model has a mass element (the body whose vibrations are to be damped) linked to the wall by means of a spring and to a massless Coulomb damper via a “contact stiffness". In Griffin’s work the normal load acting on the Coulomb damper was kept constant. We introduce cyclic amplitude of the normal load, and phase shift between tangential and normal load. It is found that the optimization curves maintain the minimum for the mean normal load expected by Griffin’s model. However, a lower vibration amplitude is found for in-phase loading with respect to the constant load, over the entire frequency range. When the “contact stiffness" is higher than the structure stiffness (as it is generally expected), the maximum vibration decrement for in-phase loading is around 40%.

The classical Cattaneo–Mindlin problem for elastic halfplanes is extended for a Griffith condition for inception of slip, and otherwise following the standard Coulomb law in the sliding zone. A general solution is found using the idea of superposing normal contact pressure distributions for arbitrary 2D geometry. In particular, the full sliding component of shear is corrected with a distribution in the stick region which is formally equivalent to a JKR solution for the normal contact problem insisting on the stick area. We show that geometry affects the apparent friction coefficient (the maximum tangential load at the inception of slip), since a sudden transition to slip occurs when the stick region reaches a critical size which corresponds to the phenomenon of pull-off in the JKR solution. Example solutions are given for Hertzian geometry, power law punches and a sinusoidal profile.