Two surfaces are “sticky” if breaking their mutual contact requires a finite tensile force. At low fractal dimensions D, there is consensus stickiness does not depend on the upper truncation ...frequency of roughness spectrum (or “magnification”). As debate is still open for the case at high D, we exploit BAM theory of Ciavarella and Persson-Tosatti theory, to derive criteria for all fractal dimensions. For high D, we show that stickiness is more influenced by short wavelength roughness with respect to the low D case. BAM converges at high magnifications to a simple criterion which depends only on D, in agreement with theories that includes Lennard-Jones traction-gap law, while Persson-Tosatti disagrees because of its simplifying approximations.
•We study the stickiness of randomly rough surfaces for the case at high fractal dimension.•We exploit BAM theory and Persson-Tosatti theory to derive two stickiness criteria in the case of high fractal dimension.•We show that stickiness is reduced by increasing the fractal dimension.•We obtain BAM stickiness criterion that holds for any fractal dimensions, showing converging results in the fractal limit.•BAM theory is in qualitatively agreement with rough contact theories where Lennard-Jones adhesive law is considered.
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.
The classical Palmgren‐Miner (PM) rule, despite clearly approximation, is commonly applied for the case of variable amplitude loading, and to date, there is no simple alternative. In the literature, ...previous authors have commented that the PM hypothesis is based on an exponential fatigue crack growth law, ie, when da/dN is proportional to the crack size a, the case that includes also Paris law for m=2, in particular. This is because they applied it by updating the damage estimate during the crack growth.
It is here shown that applying PM to the “initial” and nominal (Stress vs Number of cycles) curve of a cracked structure results exactly in the integration of the simple Paris power law equation and more in general to any crack law in the form da/dN=HΔσhan. This leads to an interesting new interpretation of PM rule. Indeed, the fact that PM rule is often considered to be quite inaccurate pertains more to the general case when propagation cannot be simplified to this form (like when there are distinct initiation and propagation phases), rather than in long crack propagation. Indeed, results from well‐known round‐robin experiments under spectrum loading confirm that even using modified Paris laws for crack propagation, the results of the “noninteraction” models, neglecting retardation and other crack closure or plasticity effects due to overloads, are quite satisfactory, and these correspond indeed very closely to applying PM, at least when geometrical factors can be neglected. The use of generalized exponential crack growth, even in the context of spectrum loading, seems to imply the PM rule applies. Therefore, this seems closely related to the so‐called lead crack fatigue lifing framework. The connection means however that the same sort of accuracy is expected from PM rule and from assuming exponential crack growth for the entire lifetime.
Due to the nonlinearity of the Coulomb friction law, even the simplest models of interfaces in contact show a very rich dynamic solution. It is often desirable, especially if the frequency of loading ...is only a fraction of the first natural frequency of the system, to replace a full dynamic analysis with a quasi-static one, which obviously is much simpler to obtain. In this work, we study a simple Coulomb frictional oscillator with harmonic tangential load, but with constant normal load. It is found that the quasi-static solution (which has only 2 stops) captures approximately the displacement peak as long as the forcing frequency is low enough for the dynamic solution to have 2 or, even better, more than 2 stops. Instead, the velocity peak is not correctly estimated, since the velocity becomes highly irregular due to the stick–slip stops, whose number increases without limit for zero frequency. In this sense, the classical quasi-static solution, obtaining by cancelling inertia terms in the equilibrium equations, does not coincide with the limit of the full dynamic solution at low frequencies. The difference is not eliminated by adding a small amount of viscous damping, as only with critical damping, the dynamic solution is very close to the quasi-static one. Additional discrepancies arise above a limit frequency whose value depends on the ratio of the tangential load to the limit one for sliding, and correspond to when the dynamic solution turns from 2 to 0 stop per cycle.
Friction-induced vibrations are known to affect many engineering applications. Here, we study a chain of friction-excited oscillators with nearest neighbor elastic coupling. The excitation is ...provided by a moving belt which moves at a certain velocity vd while friction is modelled with an exponentially decaying friction law. It is shown that in a certain range of driving velocities, multiple stable spatially localized solutions exist whose dynamical behavior (i.e. regular or irregular) depends on the number of oscillators involved in the vibration. The classical non-repeatability of friction-induced vibration problems can be interpreted in light of those multiple stable dynamical states. These states are found within a “snaking-like” bifurcation pattern. Contrary to the classical Anderson localization phenomenon, here the underlying linear system is perfectly homogeneous and localization is solely triggered by the friction nonlinearity.
•A friction-excited oscillator chain is studied with periodic boundary conditions.•Multiple, spatially localized vibrating states have been found.•Multiplicity can explain the lack of repeatability of friction-induced vibrations.•Different initial conditions lead to different localized patterns.•In the bifurcation diagram “snaking-like” bifurcations have been obtained.
The electroadhesive contact between a conductive sphere with a rigid substrate, both coated with an electrically insulating layer is studied, by adopting two solution strategies: (i) a DMT ...approximation and (ii) an iterative finite element model which accounts for the effect of the electroadhesive tractions on the deformation of the elastic solids. The contact problem is solved by varying the applied voltage and the elastic modulus of the coating layer. The two approaches (i) and (ii) give comparable results only in the limit of very low applied voltage, while they differ quantitatively and qualitatively at high voltage, as the DMT approach largely fails in predicting the repulsive contact force, which leads to greatly overestimate the macroscopic adhesive force.
•Contact between a soft sphere and a rigid substrate is studied in presence of electroadhesion.•A DMT model and a full Finite Element (FE) model have been developed.•The DMT model leads to overestimated the effect of the adhesive tractions.•For high voltage full FE and DMT simulations give quantitatively and qualitatively different results.
If the nominal contact tractions at an interface are everywhere below the Coulomb friction limit throughout a cycle of oscillatory loading, the introduction of surface roughness will generally cause ...local microslip between the contacting asperities and hence some frictional dissipation. This dissipation is important both as a source of structural damping and as an indicator of potential fretting damage. Here we use a strategy based on the Ciavarella-Jäger superposition and a recent solution of the general problem of the contact of two half spaces under oscillatory loading to derive expressions for the dissipation per cycle which depend only on the normal incremental stiffness of the contact, the external forces and the local coefficient of friction. The results show that the dissipation depends significantly on the relative phase between the oscillations in normal and tangential load—a factor which has been largely ignored in previous investigations. In particular, for given load amplitudes, the dissipation is significantly larger when the loads are out of phase. We also establish that for small amplitudes the dissipation varies with the cube of the load amplitude and is linearly proportional to the second derivative of the elastic compliance function for all contact geometries, including those involving surface roughness. It follows that experimental observations of less than cubic dependence on load amplitude cannot be explained by reference to roughness alone, or by any other geometric effect in the contact of half spaces.
Abstract In the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack ...propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.
The eigenfunction method pioneered by Galin (J Appl Math Mech 40: 981–986, 1976) is extended to provide a general solution to the transient evolution of contact pressure and wear of two sliding ...elastic half-planes, under the assumption that there is full contact and that the Archard–Reye wear law applies. The governing equations are first developed for sinusoidal profiles with exponential growth rates. The contact condition and the wear law lead to a characteristic equation for the growth rate and more general solutions are developed by superposition. The case of general initial profiles can then be written down as a Fourier integral. Decay rates increase with wavenumber, so fine-scale features are worn away early in the process. Qualitative features of the problem are governed by two dimensionless wear coefficients, which for many material combinations are small compared with unity. If one of the bodies does not wear and is non-plane, the system evolves to a non-trivial steady state in which the wearing body acquires a profile which migrates over its surface.
Various authors have studied the frictional contact problem for a simple concentrated mass under periodic forcing terms. In this paper, we give some additional closed form results for this problem ...for both the quasi-static limit and the full dynamic regime. We find in particular the regime where normal load is high enough to obtain a bounded displacement at all frequencies, which is of particular interest for “optimal” damping: in this case, the dynamic solution involves 2 stops of finite time. Contrary to the quasi-static prediction, the effect of normal load variation can decrease the peak displacement amplitude for in-phase loading up to the 80 percent. Moreover, similar to the quasi-static prediction, it can lead to a very large increase (up to more than 200 percent) for quadrature loading. Similar pattern is found for the frictional dissipation per cycle. For in-phase loading, therefore, the vibratory motion is damped more effectively, with additional beneficial effects on joint lifetime.
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