Search

International audience; The aim of this study is to investigate experimentally the transition from a rigid regime to a deformed regime for flexible discs freely advected in turbulent flows. For a given disc, the amplitude of the deformation is expected to increase when its bending modulus decreases or when the turbulent kinetic energy increases. To quantify this qualitative argument, experiments are performed where the deformation of flexible discs is measured using three cameras. The amplitude of the deformation has been characterised by the eigenvalues of the moment of inertia tensor. Experimental results exhibit a transition from a rigid regime to a deformed regime that depends on the size, the density and the flexibility of the disc and the turbulent kinetic energy. The modelling of this transition is a generalisation and an extension of the previous models used to characterise the deformation of flexible fibres in turbulent flows.

We study the fragmentation of deformable and brittle fibers in the inertial range of turbulence using laboratory experiments and numerical simulations. The fragmentation process is shown to be limited at small scales by a physical cut-off length due to fluid-structure interactions of the object with turbulence, and thus independent of the fiber brittleness. This scenario, comprehensively modeled by an evolution equation, leads to the accumulation of fragments slightly longer than the cut-off scale, as smaller fragments are too short to be deformed and broken by the turbulence. This result may improve our understanding of microplastic formation in the ocean.

We present results of a hybrid experimental, theoretical, and simulation-based investigation of the postbuckling behavior of thin elastic rods axially impacted by a projectile. We find a new postbuckling mechanism: mode coarsening. Much akin to inverse energy cascade phenomena in other nonlinear dynamic systems, energy is transferred during mode coarsening from higher to lower wave numbers-unless the rod breaks, abruptly dissipating in the course of fracture the rod's strain energy. We derive a model that provides a predictive means to capture mode coarsening in the form of a nondissipative, purely geometric force relaxation mechanism, and validate the model by means of molecular dynamics (MD) based structural dynamics simulations for rods of wood and pasta considering different thermodynamic ensembles. The scalability of theory and simulation for engineering applications opens new venues toward safe design of engineering structures subject to impact-induced risks of buckling, ranging from skyscrapers, to aerospace structures, to the crashworthiness of vehicles, for example.

International audience; We study the mechanical response, and tearing features of crêpe paper, a two-dimensional, very anisotropic material, with one direction much less stiff than the other one. Depending on how the soft direction has been pre-stretched or not, the apparent Young modulus of the material can be varied over a broad range, while its fracture energy remains unaltered. The classical tearing concertina problem shows that a macroscopic measurement (the shape of the teared region) provides a direct access to the fracture properties of the material (effective Young's modulus, and fracture energy). The overall discussion is conducted in the frame of Griffith's theory of fracture.

International audience; Fiber networks encompass a wide range of natural and man-made materials. The threads or filaments from which they are formed span a wide range of length scales: from nanometers, as in biological tissues and bundles of carbon nanotubes, to millimeters , as in paper and insulation materials. The mechanical and thermal behavior of these complex structures depends on both the individual response of the constituent fibers and the density and degree of entanglement of the network. A question of paramount importance is how to control the formation of a given fiber network to optimize a desired function. The study of fiber clustering of natural flocs could be useful for improving fabrication processes, such as in the paper and textile industries. Here, we use the example of aegagropilae that are the remains of a seagrass (Posidonia oceanica) found on Mediterranean beaches. First, we characterize different aspects of their structure and mechanical response, and second, we draw conclusions on their formation process. We show that these natural aggregates are formed in open sea by random aggregation and compaction of fibers held together by friction forces. Although formed in a natural environment, thus under relatively unconstrained conditions, the geometrical and mechanical properties of the resulting fiber aggregates are quite robust. This study opens perspectives for manufacturing complex fiber network materials. fiber network | fiber aggregation | Posidonia oceanica | fibrous material A egagropilae are a natural aggregate of fibers produced by the decomposition of leaves and roots of Posidonia ocean-ica. The fibers are entangled by sea motion until the clusters reach the shore (1) (Fig. 1). P. oceanica is an endemic plant of the Mediterranean Sea with very long and thin leaves (about 1-m long, 1-cm wide, and less than 1-mm thick). The name aega-gropilae originates from the Greek [α´ιγαγρoςα´ιγαγρoς (wild goat) and π˜ιλoςπ˜ιλoς (fur)] and refers to the resemblance between the shape of these balls and those regurgitated by goats. Natural fiber clustering occurs for different species of aquatic plants, such as the so-called seaballs that can be found on the Atlantic Ocean and lake shores (2, 3). P. oceanica meadows play an important ecological role in the preservation of Mediterranean coasts. They constitute plant barriers that promote sediment trapping and oxygen production in seabed, and the accumulated remains protect the beaches from erosion. Moreover, aegagropilae fibers are suitable materials for insulation in construction and automotive industries. After submitting them to various tests, they recently landed in the marketplace under the name of Neptutherm. Beyond the curiosity that these natural objects can provoke, aegagropilae samples found on beaches raise several fundamental questions. The first set of questions is on their formation process. How can fibers be entangled and packed by a flow without any confinement? How long does it take to form a cluster? Can one explain the size distribution of these aggregates? The second set of questions is on the cohesion of these structures. How can we relate the apparent stiffness of these balls to the interaction of the fibers and the topological properties of the network? Natural and manmade fiber networks are abundant structures and arise on a wide range of length scales. Examples may be found in both biological systems, such as the cytoskeleton of a cell (4), blood clots (5), and biological tissues (6), and technology , such as nanotube bundles (7), paper (8), textiles, and felts (9–11). The mechanical response of fiber assemblies depends on both the properties of the elementary thread and the density , connectivity, and ordering of the network. Therefore, the functional properties of these materials can be tuned by controlling their formation processes. The manufacturing of some athermal networks, such as paper, involves transport of fibers in a fluid flow (8). During this process, fibers are advected and deformed elastically, and they interact through interfiber friction (12, 13). From this perspective, aegagropilae are an archetype of these fiber networks, and understanding the clustering mechanism can shed light on the fundamental aspects of fiber aggre-gation dynamics. Here, we perform various measurements on aegagropilae to characterize their structural and mechanical properties. Our observations provide a qualitative understanding of the formation process of this fiber network. Structural Properties of Aegagropilae Aegagropilae were collected at two different locations of the Mediterranean shore: at Six Fours, France (43 • 06 03 N, 5 • 49 20 E) and on Porquerolles Island, France (43 • 00 02 N, 6 • 13 38 E) with the authorization of Port-Cros National Park. On the first beach, nearly 2,000 samples were collected to determine their size and mass distributions. To avoid any bias in the sampling caused by damage of aegagropilae by human activity, all samples were collected on a morning in winter, the day after a storm. Moreover, only balls found at a distance less than 10 m from the sea were collected, assuming that the ones located farther away from the sea might have been released by a precedent storm. At the second spot, few samples were picked up in seabed to investigate the geometrical and mechanical properties of fiber Significance Aegagropilae are centimeter-sized, nearly spherical fiber aggregate found on Mediterranean beaches. They result from aggregation and compaction of the remains of the seagrass Posidonia oceanica. We find that they possess remarkable mechanical properties, which are unexpected for a structure formed by random agitation caused by sea motion and held together solely by friction between the fibers. The study of such material offers perspectives for complex materials, such as felts and insulation materials.

A sharp transition between liquefaction and transient solidification is observed during impact on a granular suspension depending on the initial packing fraction. We demonstrate, via high-speed pressure measurements and a two-phase modeling, that this transition is controlled by a coupling between the granular pile dilatancy and the interstitial fluid pressure generated by the impact. Our results provide a generic mechanism for explaining the wide variety of impact responses in particulate media, from dry quicksand in powders to impact-hardening in shear-thickening suspensions like cornstarch., e.g. 11 pages, 4 figures, 3 supplemetal figures, one supplemental table

When impacted by a rigid body, a thin elastic membrane with negligible bending rigidity floating on a liquid pool deforms. Two axisymmetric waves radiating from the impact point propagate. First, a longitudinal wave front, associated with in-plane deformation of the membrane and traveling at constant speed, separates an outward stress-free domain from a stretched domain. Then, in the stretched domain a dispersive transverse wave travels at a speed that depends on the local stretching rate. The dynamics is found to be self-similar in time. Using this property, we show that the wave dynamics is similar to the capillary waves that propagate at a liquid-gas interface but with a surface tension coefficient that depends on impact speed. During wave propagation, we observe the development of a buckling instability that gives rise to radial wrinkles. We address the dynamics of this fluid-body system, including the rapid deceleration of an impactor of finite mass, an issue that may have applications in the domain of absorption of impact energy.

International audience; We study transverse impacts of rigid objects on a free elastic membrane, using thin circular sheets of natural rubber as experimental models. After impact, two distinct axisymmetric waves propagate in and on the sheet. First a tensile wave travels at sound speed leaving behind the wave front a stretched domain. Then, a transverse wave propagates on the stretched area at a lower speed. In the stretched area, geometrical confinement induces compressive circumferential stresses leading to a buckling instability, giving rise to radial wrinkles. We report on a set of experiments and theoretical remarks on the conditions of occurrence of these wrinkles, their dynamics and wavelength.

A cohesive object will eventually break into fragment when experiencing a strong deformation, during an impact for instance. Using necklaces of cohesive magnetized spheres suddenly expanded, we have shown that the fragmentation of this one-dimensional material results from an inverse aggregation cascade (Vledouts et al. 2015 Proc. R. Soc. A 471, 20150678. (doi:10.1098/rspa.2015.0678)). Here, we explore a variant of this process by changing the force law between the attracting spheres, using hydrogel beads linked by capillary bridges. We also investigate the role of (weak) defects in the cohesion strength and the consequences of a distribution of forces between the beads. It is found that fragment do form by a cascade of aggregations, which is interrupted earlier when the force disorder is stronger.

When severely impacted, a cohesive object deforms and eventually breaks into fragments. Cohesion forces keeping the material together and momentum driving the fragmentation couple through a complicated process involving crack propagation on a deforming substrate, so that a comprehensive scenario for the build-up of the full fragment size distribution of broken objects is still lacking. We use necklaces of cohesive particles (magnetized spheres) as an experimental model of a one-dimensional material, which we expand radially in an impulsive way. Exploring in real time the intermediate state where the particles are no longer in contact, but still in interaction as they separate, we demonstrate that the final fragments result from the self-assembly of individual particles and that their size distribution converges to a stable self-similar distribution whose parameters, interpreted from first principles, depend on the expansion and cohesion strengths.

The dynamics of Bose-Einstein condensates in a double-well magnetic trap is studied using the Gross-Pitaevskii equation (GPE) and a two-mode approximation. The self-trapping instability occurs when a sufficiently high potential barrier is formed in the centre of the trap. Close to the instability threshold, the GPE is reduced to a simple amplitude equation. In the case where weakly dissipative effects are taken into account, the condensate exhibits aperiodic oscillations which can be described by the Lorenz thermal convection model.

We study impacts of a rigid body on a thin elastic sheet floating on a liquid. When struck by a solid object of small size, the elastic sheet deforms and waves propagate in and on the membrane. The impact triggers a longitudinal elastic wave effectively stretching the membrane. The hydroelastic transverse wave that propagates in the stretched domain is similar to capillary waves on a free surface with an equivalent ‘surface tension’ that results from the stretching of the elastic membrane. Two limiting cases, for which a self-similar solution can be computed, corresponding to short and long times are identified. Surprisingly, our study reveals that the fluid–body system behaves as a regular liquid–gas interface, but with an effective surface tension coefficient that scales linearly with the impact velocity.

We consider solutions of a partial differential equation which are homogeneous in space and stationary or periodic in time. We study the stability with respect to large wavelength perturbations and the weakly nonlinear behavior around these solutions, especially when they are close to bifurcations for the ordinary differential equation governing the homogeneous solutions of the PDE. We distinguish cases where a spatial parity symmetry holds. All bifurcations occurring generically for two-dimensional ODES are treated. Our main result is that for almost homoclinic periodic solutions instability is generic.

It has been recently shown that the continuous coupling of non-linear oscillators close to an Andronov homoclinic bifurcation generically leads to two types of instabilities: a self-focusing Kuramoto like instability or a finite wavelength period doubling instability. The purpose of this paper is to study simple examples where these instabilities have been observed. It includes the coupling of two pendula, the sine-Gordon chain and the coupling of dissipative non-linear oscillators.

International audience; Broken thin brittle plates like windows and windshields are ubiquitous in our environment. When impacted locally, they typically present a pattern of cracks extending radially outwards from the impact point. We study the variation of the pattern of cracks by performing controlled transverse impacts on brittle plates over a broad range of impact speed, plate thickness and material properties, and we establish from experiments a global scaling law for the number of radial cracks incorporating all these parameters. A model based on Griffith's theory of fracture combining plate bending elastic energy and fracture energy accounts for our observations. These findings indicate how the post-mortem shape of broken samples are related to material properties and impact parameters, a procedure relevant to forensic science, archaeology or astrophysics.

International audience; We study the kinetics of a large number of organisms initially spread uniformly in a circular two-dimensional medium, at the center of which a smaller circular trap has been introduced. We take advantage of the acidophily of Paramecium caudatum, which, coming from a neutral medium, penetrates a region of moderate acidity but moves back in the opposite situation when it meets a sharp negative acidity gradient to quantify its rate of irreversible aggregation into a spot of acidified medium in water. Two regimes are distinguished: A ballistic regime characteristic of “fresh” paramecia where the organisms swim in a straight path with a well defined velocity and a Brownian regime characteristic of older paramecia where the mean free path of the organisms is smaller than the system size. Both regimes are characterized by distinct aggregation laws. They both result from a pure random trapping process that appears to have no adaptive strategy.

International audience; When a rigid cone is slowly pushed through a thin elastic sheet, the material breaks, exhibiting a network of cracks expanding in the radial direction. Experiments conducted with aluminum sheets show that the number of cracks is selected at the beginning of the perforation process and then remains stable. A simple model predicts the number of cracks as the result of a competition between the elastic energy stored in the sheet, and the energy dissipated during crack extension. We also evidence the subtle rearrangements of randomly distributed cracks into uniform radial patterns with fewer cracks. In that respect, this study exemplifies how relaxation mechanisms in fragmenting solids can attenuate the influence of defects in the material.

International audience; We construct a valveless pump consisting of a section of elastic tube and a section of rigid tube connected in a closed loop and filled with water. By periodically squeezing the elastic tube at an asymmetric location, a persistent flow around the tubes is created. This effect, called the Liebau phenomenon or valveless pumping, has been known for some time but is still not completely understood. We study the flow rates for various squeezing locations, frequencies, and elastic tube rigidities. To understand valveless pumping, we formulate a simple model that can be described by ordinary differential equations. The time series of flow velocities generated by the model are qualitatively and quantitatively similar to those seen in the experiment. The model provides a physical explanation of valveless pumping, and it allows us to identify the essential pumping mechanisms.

International audience; When an initially stretched rubber band is suddenly released at one end, an axial-stress front propagating at the celerity of sound separates a free and a stretched domain of the elastic material. As soon as it reaches the clamped end, the front rebounds and a compression front propagates backward. When the length of the compressed area exceeds Euler critical length, a dynamic buckling instability develops. The rebound is analysed using Saint-Venant's theory of impacts and we use a dynamical extension of the Euler–Bernoulli beam equation to obtain a relation between the buckled wavelength, the initial stretching and the rubber band thickness. The influence of an external fluid medium is also considered: owing to added mass and viscosity, the instability growth rate decreases. With a high viscosity, the axial-stress front spreads owing to viscous frictional forces during the release phase. As a result, the selected wavelength increases significantly.

International audience; We study the dynamics of a rigid, symmetric wing that is flapped vertically in a fluid. The motion of the wing in the horizontal direction is not constrained. Above a critical flapping frequency, forward flight arises as the wing accelerates to a terminal state of constant speed. We describe a number of measurements which supplement our previous work. These include (a) a study of the initial transition to forward flight near the onset of the instability, (b) the separate effects of flapping amplitude and frequency, (c) the effect of wing thickness, (d) the effect of asymmetry of the wing planform, and (e) the response of the wing to an added resistance. Our results emphasize the robustness of the mechanisms determining the forward flight speed as observed in our previous study.

International audience; Small flexible bodies are observed to hover in an oscillating air column. The air is driven by a large speaker at frequencies in the range 10–65 Hz at amplitudes 1–5 cm. The bodies are made of stiffened tissue paper, bent to form an array of four wings, symmetric about a vertical axis. The flapping of the wings, driven by the oscillating flow, leads to stable hovering. The hovering position of the body is unstable under free fall in the absence of the airflow. Measurements of the minimum flow amplitude as a function of flow frequency were performed for a range of self-similar bodies of the same material. The optimal frequency for hovering is found to vary inversely with the size. We suggest, on the basis of flow visualization, that hovering of such bodies in an oscillating flow depends upon a process of vortex shedding closely analogous to that of an active flapper in otherwise still air. A simple inviscid model is developed illustrating some of the observed properties of flexible passive hoverers at high Reynolds number.

The dynamics of a damped pendulum driven by a constant torque is studied experimentally and theoretically. We use this simple device to demonstrate some generic dynamical behavior including the loss of equilibrium or saddle node bifurcation with or without hysteresis and the homoclinic bifurcation. A qualitative analysis is developed to emphasize the role of two dimensionless parameters corresponding to damping and forcing.

International audience; By immersing a compliant yet self-supporting sheet into flowing water, we study a heavy, streamlined, and elastic body interacting with a fluid. We find that above a critical flow velocity a sheet aligned with the flow begins to flap with a Strouhal frequency consistent with animal locomotion. This transition is subcritical. Our results agree qualitatively with a simple fluid dynamical model that predicts linear instability at a critical flow speed. Both experiment and theory emphasize the importance of body inertia in overcoming the stabilizing effects of finite rigidity and fluid drag.

Flapping flight is ubiquitous in Nature, yet cilia and flagella, not wings, prevail in the world of micro-organisms. This paper addresses this dichotomy. We investigate experimentally the dynamics of a wing, flapped up and down and free to move horizontally. The wing begins to move forward spontaneously as a critical frequency is exceeded, indicating that ‘flapping flight’ occurs as a symmetry-breaking bifurcation from a pure flapping state with no horizontal motion. A dimensionless parameter, the Reynolds number based on the flapping frequency, characterizes the point of bifurcation. Above this bifurcation, we observe that the forward speed increases linearly with the flapping frequency. Visualization of the flow field around the heaving and plunging foil shows a symmetric pattern below transition. Above threshold, an inverted von Karman vortex street is observed in the wake of the wing. The results of our model experiment, namely the critical Reynolds number and the behaviour above threshold, are consistent with observations of the flapping-based locomotion of swimming and flying animals.

We analyze the dynamics of a weakly open Bose-Einstein condensate trapped in a double-well potential. Close to the self-trapping bifurcation, numerical simulations of the weakly irreversible one-dimensional Gross Pitaevskii equation reveal chaotic behaviors. A two-mode model is used to derive amplitude equations describing the complex dynamic of the condensate.

Some mechanisms of shape selection and fragmentation patterns of impacted or strongly solicited elastic bodies of simple geometry are reviewed. By strongly solicited we mean objects whose shape undergoes order one deformations, a situation typically encountered with soft bodies, possibly leading to fracture. We are particularly interested in the development of elastic instabilities and their relevance to interpret fragmentation experiments. We review how the shape of elastic slender objects like rods and membranes is affected by buckling instabilities when impacted, and how brittle sheets break through a well-defined pattern of cracks. Central to the understanding of this pattern is the concept of optimal fragmentation. The crack pattern of thin elastic bodies, including the diverging concertina tearing, the perforation of a thin sheet by a cone and the star shape pattern of impacted windows are optimal objects, ruled by a balance between stored elastic energy and surface creation energy.