Giuseppe Carbone

Contact mechanics and rubber friction for randomly rough surfaces with anisotropic statistical properties

In this paper we extend the theory of contact mechanics and rubber friction developed by one of us (B.N.J. Persson, J. Chem. Phys. 115, 3840 (2001)) to the case of surfaces with anisotropic surface roughness. As an application we calculate the viscoelastic contribution to the rubber friction. We show that the friction coefficient may depend significantly on the sliding direction, while the area of contact depends weakly on the sliding direction. We have carried out experiments for rubber blocks sliding on unidirectionally polished steel surfaces. The experimental data are in a good qualitative agreement with the theory.

Sticky Bio-inspired Micropillars: Finding the Best Shape

Very recently, both experimental and theoretical investigations have shown that microstructured surfaces covered with mushroom-shaped micropillars present strongly enhanced adhesive properties if compared to flat surfaces made of the same material. However, different geometries lead to different adhesive performance, and finding the optimal solution has become of utmost importance. This paper presents on which physical basis the optimal mushroom pillar shape should be sought, and it provides a relatively simple methodology to achieve the result. Calculations demonstrate that the adhesive performance of the pillar strongly depends on the geometry of the terminal plate. The best performance is achieved when the ratio s/R(i) between the plate thickness (s) and the pillar internal radius (R(i)) is close to 0.2-0.3, and the ratio R(e)/R(i) is larger than 2, where R(e) is the external radius of the plate.

Adhesive contact of rough surfaces: Comparison between numerical calculations and analytical theories

The authors have employed a numerical procedure to analyse the adhesive contact between a soft elastic layer and a rough rigid substrate. The solution to the problem, which belongs to the class of the free boundary problems, is obtained by calculating Green’s function which links the pressure distribution to the normal displacements at the interface. The problem is then formulated in the form of a Fredholm integral equation of the first kind with a logarithmic kernel. The boundaries of the contact area are calculated by requiring the energy of the system to be stationary. This methodology has been employed to study the adhesive contact between an elastic semi-infinite solid and a randomly rough rigid profile with a self-affine fractal geometry. We show that, even in the presence of adhesion, the true contact area still linearly depends on the applied load. The numerical results are then critically compared with the predictions of an extended version of Persson’s contact mechanics theory, which is able to handle anisotropic surfaces, as 1D interfaces. It is shown that, for any given load, Persson’s theory underestimates the contact area by about 50% in comparison with our numerical calculations. We find that this discrepancy is larger than for 2D rough surfaces in the case of adhesionless contact. We argue that this increased difference might be explained, at least partially, by considering that Persson’s theory is a mean-field theory in spirit, so it should work better for 2D rough surfaces rather than for 1D rough surfaces. We also observe that the predicted value of separation is in agreement with our numerical results as well as the exponents of the power spectral density of the contact pressure distribution and of the elastic displacement of the solid. Therefore, we conclude that Persson’s theory captures almost exactly the main qualitative behaviour of the rough contact phenomena.

Adhesion of Elastic Thin Films: Double Peeling of Tapes Versus Axisymmetric Peeling of Membranes

The mechanism of detachment of thin films from a flat smooth rigid substrate is investigated. In particular, analytical solutions in closed form are proposed for the double peeling of an elastic tape as well as for the axisymmetric peeling of a membrane. We show that in the case of double peeling of an endless elastic tape, a critical value of the pull-off force is found, above which the tape is completely detached from the substrate. In particular, as the detachment process advances, the peeling angle is stabilized on a limiting value, which only depends on the geometry of the tape, its elastic modulus and on the interfacial energy

Lubrication in soft rough contacts: A novel homogenized approach. Part I - Theory

\Updelta\gamma

Role of statistical properties of randomly rough surfaces in controlling superhydrophobicity.

Δγ. This predicted behavior agrees with the “theory of multiple peeling” and clarifies some aspects of this theory. Moreover, it is also corroborated by experimental results (work in progress) we are carrying out on a standard adhesive tape adhered to a smooth flat poly(methyl methacrylate) surface. In the case of the axisymmetric adhering membrane, a different behavior is observed. In such case, the system is always stable, and the detached area monotonically increases with the peeling force, i.e., the elastic membrane can sustain in principle any applied force. Results are validated by a fully numerical analysis performed with the aid of a finite element commercial software.

Adhesion tilt-tolerance in bio-inspired mushroom-shaped adhesive microstructure

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.

Biomimetic surfaces with controlled direction-dependent adhesion

We study the lubricated steady sliding contact between rough surfaces of (elastically) soft solids. A novel mean field theory of mixed lubrication is presented, which takes into account the coupled effect of asperity–asperity and asperity–fluid interactions. We calculate the fluid flow factors, and discuss the nature of the transition from the boundary lubrication regime, where the normal load is supported by the asperity–asperity interactions (sometimes mediated by boundary films), to the hydrodynamic regime, where a thin fluid film prevents direct contact between the mating surfaces.