Nouveaux types d'ondes solitaires à la surface de l'eau

Au moyen de l'excitation paramétrique de vagues de surface, nous mettons en évidence deux types nouveaux de vagues solitaires, stationnaires, hautement localisées. L'une d'entre elle est de symétrie paire, l'autre de symétrie impaire. Ces deux vagues sont de grandes amplitudes et diffèrent grandement des autres types de structures localisées mises en évidence précédemment. De plus, a notre connaissance, un onde solitaire de symétrie impaire n'avait jamais été mis en évidence auparavant

Compressions of a polycarbonate honeycomb

International audienceThe in-plane compressive response of a polycarbonate honeycomb with circular close-packed cells is considered first experimentally then analytically. Under quasi-static uniaxial compression, we observed behaviors strongly depending on the orientation: for one of the two main orientations the compression is homogeneous, while for the other the deformation localizes in a very narrow band of cells. More surprisingly, for not crushing but extreme compression, when the load is released, the deformation is reversed, the localization disappears and the polycarbonate returns to its original shape. In order to explain this strange phenomena, we develop a geometric model of this honeycomb together with an expression of the bending energy. We focus on a basic mechanical element made of an elastica triangle. We also compare our description with previous experimental studies and simulations made with similar material. Finally , to illustrate mathematically this type of behavior, we present a simple model for buckling deformations with two degrees of freedom

Dynamics of granular avalanches caused by local perturbations

Surface flow of granular material is investigated within a continuum approach in two dimensions. The dynamics is described by a non-linear coupling between the two `states' of the granular material: a mobile layer and a static bed. Following previous studies, we use mass and momentum conservation to derive St-Venant like equations for the evolution of the thickness R of the mobile layer and the profile Z of the static bed. This approach allows the rheology in the flowing layer to be specified independently, and we consider in details the two following models: a constant plug flow and a linear velocity profile. We study and compare these models for non-stationary avalanches triggered by a localized amount of mobile grains on a static bed of constant slope. We solve analytically the non-linear dynamical equations by the method of characteristics. This enables us to investigate the temporal evolution of the avalanche size, amplitude and shape as a function of model parameters and initial conditions. In particular, we can compute their large time behavior as well as the condition for the formation of shocks.Comment: 25 pages, 12 figure

Pre-avalanche instabilities in a granular pile

We investigate numerically the transition between static equilibrium and dynamic surface flow of a 2D cohesionless granular system driven by a continuous gravity loading. This transition is characterized by intermittent local dynamic rearrangements and can be described by an order parameter defined as the density of critical contacts, e.g. contacts where the friction is fully mobilized. Analysis of the spatial correlations of critical contacts shows the occurence of ``fluidized'' clusters which exhibit a power-law divergence in size at the approach of the stability limit. The results are compatible with recent models that describe the granular system during the static/dynamic transition as a multi-phase system.Comment: 9 pages, 6 figures, submitted to Phys. Rev. Let

Stress transmission in granular matter

The transmission of forces through a disordered granular system is studied by means of a geometrical-topological approach that reduces the granular packing into a set of layers. This layered structure constitutes the skeleton through which the force chains set up. Given the granular packing, and the region where the force is applied, such a skeleton is uniquely defined. Within this framework, we write an equation for the transmission of the vertical forces that can be solved recursively layer by layer. We find that a special class of analytical solutions for this equation are L\'evi-stable distributions. We discuss the link between criticality and fragility and we show how the disordered packing naturally induces the formation of force-chains and arches. We point out that critical regimes, with power law distributions, are associated with the roughness of the topological layers. Whereas, fragility is associated with local changes in the force network induced by local granular rearrangements or by changes in the applied force. The results are compared with recent experimental observations in particulate matter and with computer simulations.Comment: 14 pages, Latex, 5 EPS figure

An interdisciplinary approach towards improved understanding of soil deformation during compaction

International audienceSoil compaction not only reduces available pore volume in which fluids are stored, but it alters the arrangement of soil constituents and pore geometry, thereby adversely impacting fluid transport and a range of soil ecological functions. Quantitative understanding of stress transmission and deformation processes in arable soils remains limited. Yet such knowledge is essential for better predictions of effects of soil management practices such as agricultural field traffic on soil functioning. Concepts and theory used in agricultural soil mechanics (soil compaction and soil tillage) are often adopted from conventional soil mechanics (e.g. foundation engineering). However, in contrast with standard geotechnical applications, undesired stresses applied by agricultural tyres/tracks are highly dynamic and last for very short times. Moreover, arable soils are typically unsaturated and contain important secondary structures (e.g. aggregates), factors important for affecting their soil mechanical behaviour. Mechanical processes in porous media are not only of concern in soil mechanics, but also in other fields including geophysics and granular material science. Despite similarity of basic mechanical processes, theoretical frameworks often differ and reflect disciplinary focus. We review concepts from different but complementary fields concerned with porous media mechanics and highlight opportunities for synergistic advances in understanding deformation and compaction of arable soils. We highlight the important role of technological advances in non-destructive measurement methods at pore (X-ray tomography) and soil profile (seismic) scales that not only offer new insights into soil architecture and enable visualization of soil deformation, but are becoming instrumental in the development and validation of new soil compaction models. The integration of concepts underlying dynamic processes that modify soil pore spaces and bulk properties will improve the understanding of how soil management affect vital soil mechanical, hydraulic and ecological functions supporting plant growth

Rheophysics of dense granular materials : Discrete simulation of plane shear flows

We study the steady plane shear flow of a dense assembly of frictional, inelastic disks using discrete simulation and prescribing the pressure and the shear rate. We show that, in the limit of rigid grains, the shear state is determined by a single dimensionless number, called inertial number I, which describes the ratio of inertial to pressure forces. Small values of I correspond to the quasi-static regime of soil mechanics, while large values of I correspond to the collisional regime of the kinetic theory. Those shear states are homogeneous, and become intermittent in the quasi-static regime. When I increases in the intermediate regime, we measure an approximately linear decrease of the solid fraction from the maximum packing value, and an approximately linear increase of the effective friction coefficient from the static internal friction value. From those dilatancy and friction laws, we deduce the constitutive law for dense granular flows, with a plastic Coulomb term and a viscous Bagnold term. We also show that the relative velocity fluctuations follow a scaling law as a function of I. The mechanical characteristics of the grains (restitution, friction and elasticity) have a very small influence in this intermediate regime. Then, we explain how the friction law is related to the angular distribution of contact forces, and why the local frictional forces have a small contribution to the macroscopic friction. At the end, as an example of heterogeneous stress distribution, we describe the shear localization when gravity is added.Comment: 24 pages, 19 figure

Rheology of dense granular materials: steady, uniform flow and the avalanche regime

International audienceIn the first partwe present experimental results concerning the flowof a densely packed grain collection down a two-dimensional inclined channel. For the range of inclinations corresponding to a steady, uniform regime and to nonsliding conditions at the bottom, we obtain quasi-linear profiles of velocity, that are in contradiction with the predictions of the kinetic theory. We attribute this discrepancy to the inadequacy of the binary collision picture in the case of dense packings. We also show that the various velocity profiles obtained for different flow rates and slopes merge onto a single master curve. Arguing that continuous paths of transient contacts are effective for transporting momentum and energy through the bulk, and that the associated dissipation time is very short compared to the time associated with shearing, we succeed in explaining this scaling behaviour and the paradoxical nonzero shear rate in the vicinity of the free surface. We also show that for dense particulate flows, the dissipation is mainly due to frictional sliding. In the second part, we emphasize some remarkable features exhibited by dry grain avalanches in laboratory experiments. According to the slope angle, the rear front propagates either upwards or downwards, with velocity approximately equal to the depth averaged velocity of the avalanche. As a counterpart, in both regimes, the velocity magnitude of the head front remains of the order of twice the depth averaged avalanche velocity. We suggest simple elementary mechanisms capable of accounting for these observations. We propose then an analytical modelling aimed at describing the combined processes governing the avalanche expansion. The two solutions thatwe obtain for the growth regimes and for the avalanche shapes resembl

New types of water waves of large amplitude.

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Mise en évidence de nouveaux types de vagues de très grandes amplitudes

Au moyen d'une expérience d'excitation paramétrique d'onde de surface, nous mettons en évidence l'existence de nouveaux types d'ondes solitaires et stationnaires à la surface de l'eau. Ces ondes de grande amplitude sont très non-linéaires et l'étude théorique réalisée ne permet pas de rendre compte de la forme des vagues mais permet de comprendre l'origine du phénomène d'hystérésis observé qui est nécessaire à la compréhension des phénomènes observés. En effet, l'existence de ces ondes (dans notre configuration expérimentale) est conditionnée par la présence d'un domaine de bistabilité dans le plan amplitude d'excitation - amplitude des vagues au coeur duquel nous avons montré qu'il était possible d'avoir coexistence de deux solutions, une d'amplitude nulle et une d'amplitude non nulle. Ces expériences en géométrie Hele-Shaw ont aussi permis de mettre en évidence des ondes enveloppes qui ne sont encore décrit par aucun modèle existant. Il s'agit à notre connaissance de la première onde enveloppe stationnaire observé à la surface de l'eau. Nous mettons aussi en évidence des ondes de gravité de très grande amplitude, qui sont formées alternativement d'étoiles et de polygones. Nous montrons que la symétrie du motif (nombre de branche de l'étoile) est indépendante de la taille et de la forme du récipient vibré. Nous montrons qu'un mécanisme de couplage non-linéaire résonant à trois ondes peut expliquer cette géométrie, bien que cette possibilité fut rejetée pour des ondes purement gravitaire.By means of the parametric excitation of water waves in a Hele-Shaw cell, we report the existence of two new types of highly localized, standing surface waves of large amplitude. They are respectively of odd and even symmetries. Both solitary waves oscillate subharmonically with the forcing frequency. They are highly nonlinear, and dier strongly from the other types of localized patterns. Moreover, to our knowledge, such a solitary waves of odd symmetry has never been reported hitherto. We report a new type of standing gravity waves of large amplitude, having alternatively the shape of a star and of a polygon. This wave is observed by means of a laboratory experiment by vibrating vertically a tank. The symmetry of the star (i.e. the number of branches) is independent of the container form and size, and can be changed according to the amplitude and frequency of the vibration. We show that this wave geometry results from nonlinear resonant couplings between three waves, although this possibility has been denied for pure gravity waves up to now.NICE-Bibliotheque electronique (060889901) / SudocSudocFranceF