[Show abstract][Hide abstract] ABSTRACT: Crumpling and folding of paper are at rst sight very di erent ways of con
ning thin sheets in a small volume: the former one is random and stochastic
whereas the latest one is regular and deterministic. Nevertheless, certain
similarities exist. Crumpling is surprisingly ine cient: a typical crumpled
paper ball in a waste-bin consists of as much as 80% air. Similarly, if one
folds a sheet of paper repeatedly in two, the necessary force becomes so large
that it is impossible to fold it more than 6 or 7 times. Here we show that the
sti ness that builds up in the two processes is of the same nature, and
therefore simple folding models allow to capture also the main features of
crumpling. An original geometrical approach shows that crumpling is
hierarchical, just as the repeated folding. For both processes the number of
layers increases with the degree of compaction. We nd that for both processes
the crumpling force increases as a power law with the number of folded layers,
and that the dimensionality of the compaction process (crumpling or folding)
controls the exponent of the scaling law between the force and the compaction
ratio.
[Show abstract][Hide abstract] ABSTRACT: The packing of elastic bodies has emerged as a paradigm for the study of
macroscopic disordered systems. However, progress is hampered by the lack of
controlled experiments. Here we consider a model experiment for the isotropic
two-dimensional confinement of a rod by a central force. We seek to measure how
ordered is a folded configuration and we identify two key quantities. A
geometrical characterization is given by the number of superposed layers in the
configuration. Using temporal modulations of the confining force, we probe the
mechanical properties of the configuration and we define and measure its
effective compressibility. These two quantities may be used to build a
statistical framework for packed elastic systems.
[Show abstract][Hide abstract] ABSTRACT: The behaviour of elastic structures undergoing large deformations is the
result of the competition between confining conditions, self-avoidance and
elasticity. This combination of multiple phenomena creates a geometrical
frustration that leads to complex fold patterns. By studying the case of a rod
confined isotropically into a disk, we show that the emergence of the
complexity is associated with a well defined underlying statistical measure
that determines the energy distribution of sub-elements,``branches'', of the
rod. This result suggests that branches act as the ``microscopic'' degrees of
freedom laying the foundations for a statistical mechanical theory of this
athermal and amorphous system.
Journal of Statistical Mechanics Theory and Experiment 09/2010; 2010(11). DOI:10.1088/1742-5468/2010/11/P11027 · 2.40 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A large variety of elastic structures naturally seem to be confined into environments too small to accommodate them; the geometry of folded structures span a wide range of length-scales. The elastic properties of these confined systems are further constrained by self-avoidance as well as by the dimensionality of both structures and container. To mimic crumpled paper, we devised an experimental setup to study the packing of a dimensional elastic object in 2D geometries: an elastic rod is folded at the center of a circular Hele-Shaw cell by a centripetal force. The initial configuration of the rod and the acceleration of the rotating disk allow to span different final folded configurations while the final rotation speed controls the packing intensity. Using image analysis we measure geometrical and mechanical properties of the folded configurations, focusing on length, curvature and energy distributions.
[Show abstract][Hide abstract] ABSTRACT: The dynamics of grain ejection consecutive to a sphere impacting a granular material is investigated experimentally and the variations of the characteristics of grain ejection with the control parameters are quantitatively studied. The time evolution of the corona formed by the ejected grains is reported, mainly in terms of its diameter and height, and favorably compared with a simple ballistic model. A key characteristic of the granular corona is that the angle formed by its edge with the horizontal granular surface remains constant during the ejection process, which again can be reproduced by the ballistic model. The number and the kinetic energy of the ejected grains are evaluated and allow for the calculation of an effective restitution coefficient characterizing the complex collision process between the impacting sphere and the fine granular target. The effective restitution coefficient is found to be constant when varying the control parameters.
[Show abstract][Hide abstract] ABSTRACT: The packing of elastic sheets is investigated in a quasi two-dimensional experimental setup: a sheet is pulled through a rigid hole acting as a container, so that its configuration is mostly prescribed by the cross-section of the sheet in the plane of the hole. The characterisation of the packed configuration is made possible by using refined image analysis. The geometrical properties and energies of the branches forming the cross-section are broadly distributed. We find distributions of energy with exponential tails. This setup naturally divides the system into two sub-systems: in contact with the container and within the bulk. While the geometrical properties of the sub-systems differ, their energy distributions are identical, indicating "thermal" homogeneity and allowing the definition of effective temperatures from the characteristic scales of the energy distributions.
[Show abstract][Hide abstract] ABSTRACT: There's been a recent surge of interest in the study of low-dimensional packed elastic manifolds. In fact, the simple act of crumpling a piece of paper does require the simultaneous interaction of many fascinating mechanisms. These include energy condensation from large length scales to small singular structures, topological self-avoidance and complex phase space landscapes reminiscent of frustration in the context of glassy systems. We will present a numerical experiment modeling the folding of an elastic rod (1D) restricted to a shrinking 2D space. The confinement is obtained by preparing an initially disordered elastic line embedded in a quadratic potential. Varying the strength of this confining potential shows that many metastable states can be observed. We are interested in a statistical analysis of the emerging folded patterns. We will discuss the relevance of our results with recent theoretical models (inspired by the free-volume theory of Edwards in the context of granular matter) and recent experiments of crumpled paper. Some references: L. Bou'e et al, PRL 97 (2006) 166104, L. Bou'e and E. Katzav EPL 80 (2007) 54002, E. Katzav, M. Adda-Bedia and A. Boudaoud PNAS 103 (2006) 18900-18904.
[Show abstract][Hide abstract] ABSTRACT: The classical "channel-levees" deposit morphology observed after natural granular flows, such as rock avalanches or pyroclastic flows, is investigated in simple flow geometry laboratory experiments. Granular material is released on a inclined plane at a constant mass flow rate and image analyses allow to study the temporal evolution of both morphological and dynamical characteristics with respect to the values of the mass flow rate and the slope angle. Although the mass flow rate remains constant all along the experiment, the morphology of the flow evolves with time : the granular flow slowly enlarges while its thickness decreases. We show that the levees commonly observed along the sides of the deposit upon interruption of the flow, disappear for long flow durations. We demonstrate that the morphology of the deposit builds up during the flow, in the form of an underlying static layer layer, which can be deduced from surface velocity profiles, by imposing the same flow rule everywhere in the flow.
[Show abstract][Hide abstract] ABSTRACT: Unconfined granular flows along an inclined plane are investigated experimentally. During a long transient, the flow gets confined by quasistatic banks but still spreads laterally towards a well-defined asymptotic state following a nontrivial process. Far enough from the banks a scaling for the depth averaged velocity is obtained, which extends the one obtained for homogeneous steady flows. Close to jamming it exhibits a crossover towards a nonlocal rheology. We show that the levees, commonly observed along the sides of the deposit upon interruption of the flow, disappear for long flow durations. We demonstrate that the morphology of the deposit builds up during the flow, in the form of an underlying static layer, which can be deduced from surface velocity profiles, by imposing the same flow rule everywhere in the flow.
[Show abstract][Hide abstract] ABSTRACT: Discrete numerical simulations are performed to study the evolution of the micro-structure and the response of a granular packing during successive loading-unloading cycles, consisting of quasi-static rotations in the gravity field between opposite inclination angles. We show that internal variables, e.g., stress and fabric of the pile, exhibit hysteresis during these cycles due to the exploration of different metastable configurations. Interestingly, the hysteretic behaviour of the pile strongly depends on the maximal inclination of the cycles, giving evidence of the irreversible modifications of the pile state occurring close to the unjamming transition. More specifically, we show that for cycles with maximal inclination larger than the repose angle, the weak contact network carries the memory of the unjamming transition. These results demonstrate the relevance of a two-phases description -strong and weak contact networks- for a granular system, as soon as it has approached the unjamming transition. Comment: 13 pages, 15 figures, soumis \`{a} Phys. Rev. E
Physical Review E 06/2005; 72(5). DOI:10.1103/PhysRevE.72.051305 · 2.29 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We perform discrete numerical simulations of a granular pile undergoing quasi-static tilting cycles in the gravity eld. The volumic deformation and the granular fabric exhibit hysteretic evolutions with the slope of the free surface. When exploring the range of metastable slopes -between the angle of repose and the angle of avalanche-, the contact network is strongly affected, as evidenced by the qualitative change of the hysteresis. A specic contribution to the observed hysteresis of the weak contacts is underlined: they carry the memory of the proximity of the slope destabilization.
[Show abstract][Hide abstract] ABSTRACT: Pour comprendre les mécanismes de déstabilisation, d’arrêt et de coexistence des phases statiques (solide) et coulantes (liquide), nous réalisons expériences et simulations numériques d’empilements granulaires modèles. Trois sujets ont été abordés au cours de cette thèse.
L’étude expérimentale de la transition d arrêt d’un empilement après un écoulement de surface met en évidence l’existence de relaxations de durée bien supérieure au temps de relaxation d’un grain sous l’action de son poids. Celle-ci est constituée de phases de relaxation et de réactivations liées à des déplacements corrélés des grains, prises en compte dans un modèle statistique.
L’étude numérique d’un empilement incliné en deçà de l’angle d’avalanche met en évidence l’influence du domaine métastable –au-delà de l’angle de repos– sur ses propriétés hystérétiques au cours de cycles quasi-statiques. Le réseau des contacts faibles est très affecté par le passage dans le domaine métastable. Les corrélations entre micro-structure, contrainte et déformation sont discutées.
Enfin, l’expérience d’un écoulement non confiné sur plan incliné permet d’étudier la loi d’écoulement dans le cas de la coexistence solide-liquide. Les caractéristiques s´electionnées par l’écoulement (épaisseur, largeur, vitesse) évoluent lentement avec le temps. La prise en compte de l’existence d’une couche basale statique permet de retrouver la corrélation entre épaisseur coulante et vitesse, comme pour un écoulement confiné, et de prédire la morphologie des dépôts (présence ou non de levées).
[Show abstract][Hide abstract] ABSTRACT: Natural granular flows such as rock avalanches, debris flows or pyroclastic flows are known to spontaneously channelize through the formation of levees along their sides. We report in this paper the results of laboratory experiments aimed at understanding this phenomenon in a simple flow geometry. The experiment consists in releasing granular material on a rough inclined plane at a constant mass flow rate. The resulting unconfined granular coulee has the shape of a finger descending the slope. Using image analysis, we measure the time evolution of both the flow morphological characteristics (width and thickness) and the surface velocity field for different values of the mass flow rate and the slope angle. Surface velocity measurements reveal the presence of static zones along the sides of the flow. Our main observation is that although the input mass flow rate remains constant during the whole experiment, the coulee never reaches a stationary state. On the contrary, the flow morphological characteristics constantly evolve with time : the granular flow slowly enlarges while its thickness decreases. If the flow is maintained for a sufficiently long time, it finally distabilizes leading to the formation of a wavy pattern along the sides of the coulee. As a result of this non-stationary flow dynamics, the final deposit morphology strongly depends on the duration of the flow. If the flow duration is short, the deposit exhibits a classical levees/channel morphology. However the levee thickness progressively decreases when the flow duration is increased. In the case of a very long flow, the levees eventually vanish. Systematic comparisons between numerical and experimental modelisations, especially on the transient dynamics of the levees/channel morphology might provide new constraints on the frictionnal constitutive behaviour of avalanches.
[Show abstract][Hide abstract] ABSTRACT: We study experimentally the relaxation towards mechanical equilibrium of a granular pile which has just experienced an avalanche and discuss it in the more general context of the granular jamming transition. Two coexisting dynamics are observed in the surface layer: a short time exponential decay consisting in rapid and independent moves of grains and intermittent bursts consisting in spatially correlated moves lasting for longer time. The competition of both dynamics results in long-lived intermittent transients, the total duration of which can late more than a thousand of seconds. We measure a two-time relaxation function, and relate it via a simple statistical model to a more usual two-time correlation function which exhibits strong similarities with auto-correlation functions found in aging systems. Localized perturbation experiments also allow us to test the pile surface layer receptivity. Comment: 9 pages, 10 figures
Physics of Condensed Matter 05/2003; DOI:10.1140/epjb/e2003-00322-1 · 1.35 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the transition from static to flowing granular pile in a model experimental system, namely a quasi-2-dimensional layer of iron beads in a rotating drum. Three kinds of experiments are conducted. The most classical one consists in driving the drum at such a low velocity that the granular pile exhibits a typical intermittent regime between the so-called angle of repose and the angle of avalanche. Having precisely defined and measured these angles and their statistical properties, we then focus on the relaxation towards equilibrium of a previously shaken pile. The dynamics exhibits both exponential decay and long-lived rearrangement dynamics. Finally, we investigate the response in micro-displacements of the pile below the angle of respose, when disturbed by a falling bead.
[Show abstract][Hide abstract] ABSTRACT: Natural slopes destabilization and gravitational flows endanger local buildings and populations. Prevention of these natural risks requires a better understanding of elementary mecanisms, which can be studied in a model granular medium. Our experiment examines the quasi-static relaxation of a pile of iron beads following the occurence of an avalanche. The pile is set up in a rotating drum. Avalanches are created by rotating the drum. After a given avalanche, the drum is stopped and the pile slope is driven to theta_i
[Show abstract][Hide abstract] ABSTRACT: Although the nature of the perturbations leading to a slope failure have long been identified (intense rainfall, rapide snowmelt,earthquake shaking, volcanic eruption, \ldots), the detailed mechanisms by which these perturbations affect the slope are still far from being understood. The natural media involved in those events (poorly sorted sediments partially saturated with water) are quite complex. However, all these natural media imply multicontacts granular interactions. In this perspective, studying the stability of a dry granular pile provides a powerfull paradigm for the analysis of natural events. To adress this problem, we study experimentally the response of a granular pile submitted to an external perturbation. The experimental setup consists of a rotating cylinder of diameter D = 45 cm half-filled with monodisperse metallic beads of diameter 3 mm. The granular pile is confined between two parallel glass endwalls separated by a gap whose width b is equal to 22 mm. The slope of the pile is set by rotating the drum. The pile is then perturbated by projecting a single bead on its free surface. Using an optical method based on the modification of the light intensity reflected by the sand pile, we determine precisely the area of the pile plastically deformed by the perturbation. The shape and the size of the deformed area are then studied as a function of the slope of the pile and velocity of the incident bead. The results show that the perturbated area increases strongly when the slope approaches the repose angle.