The frictional properties of a rough contact interface are controlled by its area of real contact, the dynamical variations of which underlie our modern understanding of the ubiquitous rate-and-state friction law. In particular, the real contact area is proportional to the normal load, slowly increases at rest through aging, and drops at slip inception. Here, through direct measurements on various contacts involving elastomers or human fingertips, we show that the real contact area also decreases under shear, with reductions as large as 30[Formula: see text], starting well before macroscopic sliding. All data are captured by a single reduction law enabling excellent predictions of the static friction force. In elastomers, the area-reduction rate of individual contacts obeys a scaling law valid from micrometer-sized junctions in rough contacts to millimeter-sized smooth sphere/plane contacts. For the class of soft materials used here, our results should motivate first-order improvements of current contact mechanics models and prompt reinterpretation of the rate-and-state parameters.

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 micro-scales, 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.

In humans, the tactile perception of fine textures (spatial scale <200 micrometers) is mediated by skin vibrations generated as the finger scans the surface. To establish the relationship between texture characteristics and subcutaneous vibrations, a biomimetic tactile sensor has been designed whose dimensions match those of the fingertip. When the sensor surface is patterned with parallel ridges mimicking the fingerprints, the spectrum of vibrations elicited by randomly textured substrates is dominated by one frequency set by the ratio of the scanning speed to the interridge distance. For human touch, this frequency falls within the optimal range of sensitivity of Pacinian afferents, which mediate the coding of fine textures. Thus, fingerprints may perform spectral selection and amplification of tactile information that facilitate its processing by specific mechanoreceptors.

We develop two new continuum contact models for coupled adhesion and friction, and discuss them in the context of existing models proposed in the literature. Our new models are able to describe sliding friction even under tensile normal forces, which seems reasonable for certain adhesion mechanisms. In contrast, existing continuum models for combined adhesion and friction typically include sliding friction only if local contact stresses are compressive. Although such models work well for structures with sufficiently strong local compression, they fail to capture sliding friction for soft and compliant systems (like adhesive pads), for which the resistance to bending is low. This can be overcome with our new models. For further motivation, we additionally present experimental results for the onset of sliding of a smooth glass plate on a smooth elastomer cap under low normal loads. As shown, the findings from these experiments agree well with the results from our models. In this paper we focus on the motivation and derivation of our continuum contact models, and provide a corresponding literature survey. Their implementation in a nonlinear finite element framework as well as the algorithmic treatment of adhesion and friction will be discussed in future work.

We describe a 2D spring-block model for the transition from static to kinetic friction at an elastic slider/rigid substrate interface obeying a minimalistic friction law (Amontons-Coulomb). By using realistic boundary conditions, a number of previously unexplained experimental results on precursory micro-slip fronts are successfully reproduced. From the analysis of the interfacial stresses, we derive a prediction for the evolution of the precursor length as a function of the applied loads, as well as an approximate relationship between microscopic and macroscopic friction coefficients. We show that the stress build-up due to both elastic loading and micro-slip-related relaxations depend only weakly on the underlying shear crack propagation dynamics. Conversely, crack speed depends strongly on both the instantaneous stresses and the friction coefficients, through a non-trivial scaling parameter.Frictional interfaces are important in many areas of science and technology, including seismology [2], biology [3, 4] and nanomechanics [5]. Whereas a satisfactory picture of the steady sliding regime of such interfaces has been developed during the last twenty years [6][7][8], the dynamics of the transition from static to kinetic friction remains elusive. During the last decade, a renewed interest has grown in such transitions, due to experimental studies that directly measured the local dynamics of frictional interfaces [9][10][11][12][13]. They have shown that macroscopic sliding occurs only after shear crack-like micro-slip fronts have spanned the entire contact interface.Experimentally, micro-slip front nucleation, propagation and arrest was shown to be controlled by the instantaneous stress field at the interface. Fronts nucleate preferentially at the trailing edge of the contact area [9,11,[14][15][16][17], an effect explained either by the enhanced shear stress near the loading point in side-driven systems [11,14,16,18] or by a friction-induced pressure asymmetry in top-driven systems [9,19]. Fronts can arise well below the macroscopic static friction threshold and arrest before the whole contact area has ruptured [14][15][16]. The length and number of these precursors depends on the precise way in which shear [14] and normal [16] forces are applied. Moreover, precursors are associated with significant changes in the spatial distribution of the real contact area [14], a quantity related to the local interfacial pressure. Finally, the propagation speed of micro-slip fronts, which covers a wide range [9][10][11]20], correlates with the local shear to normal stress ratio at nucleation [17].Theoretically, some aspects of these observations have been studied using one-dimensional (1D) models. The conditions leading to a large range of front velocities were addressed using a 1D spring-block model with a timedependent friction law [18]. The role of an asymmetric normal loading on the length of precursors was considered using a 1D spring-block model with Amontons-Coulomb (A-C) friction and different normal forces ascribed...

58 pages, 17 figures, 2 tables. Accepted in Journal of Volcanology and Geothermal ResearchInternational audienceIn this paper, we develop a new axisymmetric analytic model of surface uplift upon sills and laccoliths, based on the formulation of a thin bending plate lying on an elastic foundation. In contrast to most former models also based on thin bending plate formulation, our model accounts for (i) axi-symmetrical uplift, (ii) both upon and outside the intrusion. The model accounts for shallow intrusions, i.e. the ratio a/h > 5 where a and h are the radius and depth of the intrusion, respectively. The main parameter of the model is the elastic length l, which is a function of the elastic properties of the bending plate and of the elastic foundation. The model exhibits two regimes depending on the ratio a/l. When a/l < 5, the uplift spreads over a substantial domain compared to that of the intrusion. In contrast, when a/l > 5, the uplift is mostly restricted upon the intrusion. When the elastic foundation is very sti ff, our model converges towards that of a clamped plate. We provide, as supplementary material, a Matlab function that calculates the surface uplift from the set of system and control parameters. We discuss three possible applications of our model: (i) The model can be used to describe sill propagation by introducing a propagation criterion. For realistic values, our model reproduces well the behavior of horizontal intrusions simulated in experiments; (ii) The model can also be used to compute the critical size of saucer-shaped sills. It shows, for instance, that a soft elastic foundation favors the horizontal spreading of sills before they form inclined sheets; (iii) We show that the classical Mogi point source model cannot be used to constrain sill properties from the surface uplift. We thus propose that our model can be used as a valuable alternative to both simple analytical models like Mogi's and more complex numerical models used to analyze ground deformation resulting from sill intrusions in active volcanoes

True contact between randomly rough solids consists of myriad individual micro-junctions. While their total area controls the adhesive friction force of the interface, other macroscopic features, including viscoelastic friction, wear, stiffness and electric resistance, also strongly depend on the size and shape of individual micro-junctions. Here we show that, in rough elastomer contacts, the shape of micro-junctions significantly varies as a function of the shear force applied to the interface. This process leads to a growth of anisotropy of the overall contact interface, which saturates in macroscopic sliding regime. We show that smooth sphere/plane contacts have the same shearinduced anisotropic behaviour as individual micro-junctions, with a common scaling law over four orders of magnitude in initial area. We discuss the physical origin of the observations in the light of a fracture-based adhesive contact mechanics model, described in the companion article, which captures the smooth sphere/plane measurements. Our results shed light on a generic, overlooked source of anisotropy in rough elastic contacts, not taken into account in current rough contact mechanics models.

Dynamic fracture experiments were performed in PMMA over a wide range of velocities and reveal that the fracture energy exhibits an abrupt 3-folds increase from its value at crack initiation at a well-defined critical velocity, below the one associated to the onset of micro-branching instability. This transition is associated with the appearance of conics patterns on fracture surfaces that, in many materials, are the signature of damage spreading through the nucleation and growth of microcracks. A simple model allows to relate both the energetic and fractographic measurements. These results suggest that dynamic fracture at low velocities in amorphous materials is controlled by the brittle/quasi-brittle transition studied here.PACS numbers: 46.50.+a, 62.20.M-, 61.43.-j Dynamic fracture drives catastrophic material failures. Over the last century, a coherent theoretical framework, the so-called Linear Elastic Fracture Mechanics (LEFM) has developed and provides a quantitative description of the motion of a single smooth crack in a linear elastic material [1]. LEFM assumes that all the mechanical energy released during fracturing is dissipated at the crack tip. Defining the fracture energy Γ as the energy needed to create two crack surfaces of a unit area, the instantaneous crack growth velocity v is then selected by the balance between the energy flux and the dissipation rate Γv. This yields [1]:where c R and E are the Rayleigh wave speed and the Young modulus of the material, respectively, and K(c) is the Stress Intensity Factor (SIF) for a quasi-static crack of length c. K depends only on the applied loading and specimen geometry, and characterizes entirely the stress field in the vicinity of the crack front. Equation (1) describes quantitatively the experimental results for dynamic brittle fracture at slow crack velocities [2]. However, large discrepancies are observed in brittle amorphous materials at high velocities [3][4][5][6]. In particular (i) the measured maximum crack speeds lie in the range 0.5 − 0.6c R , i.e. far smaller than the limiting speed c R predicted by Eq. (1) and (ii) fracture surfaces become rough at high velocities (see [3,4] for reviews). It has been argued [7] that experiments start to depart from theory above a critical v b ≃ 0.4c R associated to the onset of micro-branching instabilities [8]: for v > v b the crack motion becomes a multi-cracks state. This translates into (i) a dramatic increase of the fracture energy Γ at v b , due to the increasing number of micro-branches propagating simultaneously and (ii) a non-univocal relation between Γ and v [7]. The micro-branching instability hence yielded many recent theoretical efforts [9]. However, a number of puzzling observations remain at smaller velocities. In particular, even for velocities much lower than v b , (i) the measured dynamic fracture energy is generally much higher than that at crack initiation [7,[10][11][12] and (ii) fracture surfaces roughen over length scales much larger than the microstructure scale ("mist" patterns...