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%, 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.
True contact between randomly rough solids consists of myriad individual microjunctions. 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 microjunctions. We show that, in rough elastomer contacts, the shape of microjunctions 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 the macroscopic sliding regime. We show that smooth sphere-plane contacts have the same shear-induced anisotropic behavior as individual microjunctions, with a common scaling law over 4 orders of magnitude in the initial area. We discuss the physical origin of the observations in 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.
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 microscales, 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.
Display omitted
•Modelling of and experiment on the evolution of contact area between soft solids under shear.•Computational finite-deformation model combining non-adhesive contact and non-linear ...elasticity.•Anisotropic area reduction quantitatively reproduced by the model with no adjustable parameter.•Three elementary mechanisms revealed: local contact lifting (main contributor), contact laying and in-plane deformation.•The findings are supported by an original experiment employing particle-tracking analysis.
Display omitted
Solid contacts involving soft materials are important in mechanical engineering or biomechanics. Experimentally, such contacts have been shown to shrink significantly under shear, an effect which is usually explained using adhesion models. Here we show that quantitative agreement with recent high-load experiments can be obtained, with no adjustable parameter, using a non-adhesive model, provided that finite deformations are taken into account. Analysis of the model uncovers the basic mechanisms underlying anisotropic shear-induced area reduction, local contact lifting being the dominant one. We confirm experimentally the relevance of all those mechanisms, by tracking the shear-induced evolution of tracers inserted close to the surface of a smooth elastomer sphere in contact with a smooth glass plate. Our results suggest that finite deformations are an alternative to adhesion, when interpreting a variety of sheared contact experiments involving soft materials.
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.
In 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 stiff, 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.
Display omitted
► New analytical model for surface uplift induced by shallow axisymmetric sill ► Model is based on thin elastic plate lying on deformable elastic foundation ► Model exhibits two regimes depending on a/l (a: sill radius; l: elastic length scale) ► Model reproduces observations for intrusion and saucer-shaped sill emplacement ► We provide a Matlab function that calculates the surface uplift from the model parameters
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 microslip 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 buildup due to both elastic loading and microslip-related relaxations depends 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 nontrivial scaling parameter.
Digital Image Correlation is used to study the micromechanics of a multi-contact interface formed between a rough elastomer and a smooth glass surface. The in-plane elastomer deformation is monitored ...during the incipient sliding regime,
i.e.
the transition between static and sliding contact. As the shear load is increased, an annular slip region, in coexistence with a central stick region, is found to progressively invade the contact. From the interfacial displacement field, the tangential stress field can be further computed using a numerical inversion procedure. These local mechanical measurements are found to be correctly captured by Cattaneo and Mindlin (CM)'s model. However, close comparison reveals significant discrepancies in both the displacement and stress fields that reflect the oversimplifying hypothesis underlying CM's scenario. In particular, our optical measurements allow us to exhibit an elasto-plastic-like friction constitutive equation that differs from the rigid-plastic behavior assumed in CM's model. This local constitutive law, which involves a roughness-related length scale, is consistent with the model of Bureau
et al.
(Proc. R. Soc. London, Ser. A
459
, 2787 (2003)) derived for homogeneously loaded macroscopic multi-contact interfaces, thus extending its validity to mesoscopic scales.
Graphical abstract
"Captain Scheibert's book was available only in German until W. S. Poole edited the present version. A member of the Prussian army since 1849, and 'well known as an authority on fortifications, ' ...Scheibert was sent to America 'to study the effect of rifled cannon fire on earth, masonry, and iron, and the operation of armor on land and at sea.' The captain preferred to observe the South rather than the North at war. 'If there ever was a foreign Rebel, ' Mr. Poole asserts, 'he was one.' Scheibert, impressed with the South's 'enormous energy' and 'amazed at the industry of a patriotic people, ' was cordially received by President Davis and Generals Lee, Jackson, Beauregard, and Stuart. The vivid impressions, observations, and characterizations of a Prussian captain are a significant commentary on the engagements at Chancellorsville, Brandy Station, and Gettysburg, on blockade running, and on the spirit of the people and their military genius."—Journal of Southern History
PDF
