Les régions de montagne sont parfois le siège de phénomènes dévastateurs brutaux, tels que les éboulements, les glissements de terrains, ou encore les avalanches. Fondamentalement, ces phénomènes sont issus de la rupture d’un volume de matériau qui va alors s’écouler sous l’effet de son poids propre. Prévoir ces phénomènes impose donc de mieux décrire la phase initiale de rupture. Ce travail de thèse s’inscrit dans cette volonté, en considérant le cas très général de la rupture dans un milieu granulaire. Pour cela, des simulations numériques utilisant une méthode aux éléments discrets ont été mises en œuvre, afin de vérifier la pertinence des critères usuels de rupture et d’instabilité. Dans un second temps, des analyses plus fines basées sur le travail du second ordre calculé à partir des variables microscopiques ont été menées afin de cerner comment évolue la microstructure de l’assemblage granulaire juste avant et pendant la rupture. Finalement, l’influence du chemin de chargement et des paramètres de contrôle sur la nature (effective ou non effective) et le mode (diffus ou localisé) de rupture a été examinée à travers une série d’essais biaxiaux sur deux échantillons numériques bidimensionnels (dense et moyennement dense). / Landslides and avalanches are the most common brutal and devastating natural hazards in mountain regions. Basically, these phenomena are derived from the failure of a material volume which will then flow under the effect of its own weight. Therefore, predicting these phenomena requires a better description of the initial phase of failure. This work comes within this willingness, considering the very general case of failure in granular media. For this purpose, numerical simulations using a discrete element method were carried out in order to investigate the relevance of the common failure and instability criteria. In a second step, more detailed analyses based on the second order work computed from the microscopic variables were conducted in order to describe the evolution of the microstructure of a granular assembly just before and during the failure. Finally, the influence of the loading path and the control parameters on the nature (effective or non-effective) and the mode (diffuse or localized) of failure was discussed through a series of biaxial tests performed on two-dimensional numerical samples depicting respectively a dense and a medium dense dry sand.

L’hydrogène est une solution chimique de stockage d’énergie électrique intéressante. En effet, l’hydrogèneproduit devient un vecteur d’énergie utilisable de différentes façons. Pour développer l’industrie hydrogène,sa production, son stockage et sa consommation doivent être étudiés et optimisés.Cette thèse traite du stockage solide d’hydrogène dans des hydrures métalliques. Dans cette technologie,l’hydrogène est piégé à l’intérieur d’un matériau métallique selon une réaction chimique réversibleexothermique. L’hydrogène peut être libéré selon la réaction inverse, endothermique. Les performances dece stockage sont liées au choix du matériau, à la gestion des transferts thermiques et au système utilisé. Sesgrands avantages sont sa compacité énergétique et la sécurité d’un tel stockage. L’inconvénient majeur vientdu poids du système. Lors de l’absorption de l’hydrogène dans le matériau, ce dernier augmente de volume.Pour pouvoir dimensionner les réservoirs à hydrures métalliques, il est nécessaire de connaître les contraintesgénérées pas ce gonflement. Le confinement du matériau dans une enceinte étanche doit être garanti. Lecyclage entre les étapes de gonflement dégonflement dûs aux stockage/dé-stockage de l’hydrogène dans unhydrure métallique est appelé la respiration de l’hydrure.Ce travail de recherche commence par rappeler l’état de l’art sur l’hydrogène et les hydrures métalliques.Dans le second chapitre, le matériau sélectionné, LmNiCoMnAl , est caractérisé. Les deux chapitres suivantsprésentent l’étude expérimentale de la respiration en conditions oedométriques à contrainte imposée et dansun volume fixe. Le chapitre cinq présente les travaux de simulation numérique par éléments discrets. Lesgrains, modélisés sous forme de clusters, sont placés dans différentes conditions aux limites avec différentscoefficients de frottement.Les résultats des expériences complètent les travaux précédents sur d’autres matériaux. Contrairementau Ti-Cr-V, le LaNiCoMnAl voit sa densité diminuer au cours de la respiration pour les contraintes deconfinement utilisées. Le taux de décroissance de la densité diminue quand la contrainte de confinementaugmente. Quand l’échantillon est placé dans un volume fixe, les contraintes développées par le matériauaugmentent avec la quantité de matériau introduite dans le volume. La simulation numérique a permis demontrer qu’une dédensification est observée pour des niveaux de contrainte intermédiaires quand le coefficientde frottement augmente, confirmant l’hypothèse que les paramètres matériaux ont une importance dans lecomportement macroscopique des hydrures métalliques pendant la respiration. / Hydrogen can be used as a storage for electric energy. Hydrogen may become an energy vector, whichcould be used and transported easily. For the hydrogen sector to develop and mature, production, storageand consumption should be researched and optimized.This PhD is dedicated to hydrogen solid storage in metal hydride. This technology consists in usinga reversible and exothermic chemical reaction between an alloy and hydrogen. The hydrogen is capturedinside the metal lattice and can be released with the endothermic opposite reaction. The main factors whichimpact the performance of this technology are the choice of material, the heat flow management and thesystem used. Its main advantages lay on safety and energy compactness. Its main drawbacks come from theweight of the system. When the material absorb hydrogen, its volume increases. To contain this materialin an airtight environment, it is mandatory to know how stress develop on the container that contains thematerial. The cycles of dilatation and contraction of the material, when it is loading or unloading hydrogen,is called breathing.This research begins with a large spectrum presentation of hydrogen. Then comes a chemical and structuralcharacterization of the material : LaNiCoMnAl. Its Composition-Temperature-Pressure characteristicsare given. The material exhibits granular properties and is structurally characterize using laser grain sizing,shape measurement and X-Ray tomography. The typical length scale of LaNiCoMnAl particles is 20 micrometers.The third and fourth chapters are concerned with the experimental behavior. A sample is placed ina stress controlled environment where its density is measured during cycling. The other experiment places asample in a fixed volume. In that case, the stress exerted on the material is recorded and measured duringcycling. In the last chapter, numerical simulations using the Discrete Element Method are used. The materialis modeled by X shaped clusters and studied with different friction parameters and boundary conditions.Following other works done on other materials, these experiment showed a different behavior of LaNi-CoMnAl compared to Ti-Cr-V. During breathing, LaNiCoMnAl exhibits a decrease in density even whensubmitted to a relatively large stress. The rate at which the density decreases is lowered when the confinementpressure increases. When the material is placed in a fixed volume, the stress increases with increasingpoured mass. Numerical simulations show a decrease in density when the friction parameter is high enough.It validates the hypothesis that material parameters play a major role in the macroscopic behavior of metalhydride during breathing.

Au cours de cette thèse expérimentale et numérique nous avons étudié le comportement d’un empilement de grains dans deux situations différentes. Dans une première partie, une piste en sable est soumise au passage répété de véhicules, sous certaines conditions un motif régulier de rides apparaît spontanément : c’est l’instabilité de tôle ondulée. Ce phénomène, très répandu sur les routes en terre ou en gravier, est bien sûr très gênant pour les automobilistes mais est aussi très dangereux à cause des pertes d’adhérence qu’il provoque. Nous avons alors reproduit ce phénomène à l’échelle du laboratoire et également dans des simulations numériques de dynamique moléculaire de sphères molles. Grâce à ces outils expérimentaux et numériques nous avons pu mettre en évidence certaines propriétés de l’instabilité. Nous avons notamment mesuré la relation de dispersion des rides et mis en évidence que ce phénomène suit une instabilité de type fourche super-critique. En mesurant les contraintes agissant sur le véhicule nous avons alors pu construire une analyse de stabilité linéaire prédisant quantitativement le seuil de l’instabilité ainsi que la longueur d’onde du motif. Enfin, nous avons étudié des cas plus complexes où différents véhicules circulaient simultanément sur la piste. Nous avons également considéré des cas où la piste était humide et donc cohésive. Dans une seconde partie, nous avons étudié le comportement d’un silo rempli de grains soumis à des variations de température. On observe alors un lent fluage de la colonne que nous avons caractérisé. Deux régimes de fluage sont observés selon l’amplitude des cycles de température et nous avons obtenu une expression de la température critique séparant les deux régimes en fonction des paramètres microscopiques des grains (élasticité et rugosité de surface). Nous avons également étudié le mouvement individuel de chaque grain afin d’interpréter la dynamique macroscopique de l’empilement. / In this experimental and numerical thesis we have studied the behavior of a granular assembly in two different situations. In the first part, a sand track is subjected to repeated passages of vehicles, under certain conditions a regular pattern of ripples appears spontaneously: this is known as the washboard road instability. This phenomenon, very common on dirt roads, is of course annoying for drivers but is also very dangerous because of the lack of adhesion it causes. We reproduced this instability with a laboratory scale set-up and also thanks to soft spheres molecular dynamics simulations. With these experimental and numerical tools we have highlighted some properties of instability. In particular, we have measured the dispersion relation of the pattern and shown that this phenomenon follows pitchfork instability. By measuring the stress acting on the vehicle we were then able to build a linear stability analysis that predicts quantitatively the threshold of the instability and the wavelength of the pattern. Finally, we have studied more complex cases where several vehicles were simultaneously on the track. We have also considered the case where the track was wet and therefore cohesive. In a second part, we have studied the behavior of a silo filled with grains subjected to temperature variations. A slow creep motion of the grains in the column is observed. Two flow regimes are observed according to the amplitude of temperature cycles. We obtained an expression of the critical temperature between the two regimes as a function of the microscopic parameters of the grains (elasticity and surface roughness). We have also studied the motion of each individual grain in order to interpret the macroscopic dynamics of the pile.

Nous nous intéressons à l'écoulement de milieux granulaires cohésifs soumis à des vibrations horizontales en vue d'une application au remplissage des moules de presse. L'effet des vibrations est analysé pour un grain ou un milieu granulaire déposé sur un plan incliné et un milieu granulaire contenu dans une conduite verticale de section constante. Pour un grain polyédrique, trois régimes sont identifiés : stick, stick-slip et slip. Un modèle basé sur le bilan des forces appliquées à un grain a permis de préciser les limites de ces trois domaines. La vitesse des grains tend vers une asymptote lorsque l'inclinaison est inférieure à 0,7 fois l'angle de frottement entre les grains et le plan. Par ailleurs, l'inertie du grain conduit à une réduction de l'amplitude de son oscillation lorsque l'accélération augmente. La comparaison modèle-expérience permet d'estimer le coefficient de frottement. Pour un milieu granulaire de faible épaisseur, nous retrouvons les mêmes tendances. Les milieux granulaires épais sont le lieu de forts cisaillements provoquant leur étalement très rapide. En conduite verticale, une compétition s'établit entre les déplacements horizontal et vertical des particules. Selon l'inertie, les vibrations appliquées pourront conduire soit à une dilatance soit à une compaction. Cette dernière provient du déplacement de la conduite et du milieu granulaire en sens opposé pendant une partie d'une période de vibration. Si le phénomène de compaction atteint le centre de la conduite, il se forme des arches qui bloquent l'écoulement. Les observations faites à l'échelle mésoscopique permettent d'interpréter les vitesses d'écoulement mesurées à l'échelle macroscopique. / With the target to improve the feeding step during the moulding process, we study the flow of cohesive granular matter submitted to vibration. Vibration effects are first analyzed on the sliding motion of a single particle on inclined plane and also on granular matter sample deposited on an inclined plane or in a vertical funnel. For a single particle, three regimes are identified: stick, stick-slip and slip regimes. A simple model based on the movement equation of one grain allows to determinate the limits between the three regimes. The grain velocity reaches asymptote when the plane inclination is below 0.7 times the friction angle between the grain and the substrate. Otherwise, when the acceleration increases, the grain inertia leads to reduce the transverse amplitude of the grain oscillation motion. The comparison between experimental and numerical results allows to estimate a value for the friction coefficient parameter. For a granular sample, we find the same tendencies. Thick granular layers are submitted to high shear, causing a fast spreading. In vertical funnel, there is a competition between vertical and horizontal motions. Depending on granular inertia, submitted vibrations could lead to dilatancy due to the shear or lead to compaction. This compaction is due to an opposite motion direction between the sample and the funnel during one part of the period vibration. If the compaction reaches the center of the funnel, arches are formed and jammed the flow. Observations realized at mesoscopic scale allow to interpret flow velocities measured at macroscopic scale.

Active matter refers to systems driven out of thermal equilibrium by the uptake and dissipation of energy directly at the level of the individual constituents, which then undergo systematic movement in a direction decided by their own internal state. This category of nonequilibrium systems was defined as the physical model of motile, metabolizing matter, but the definition has a wider application. In this thesis we work with monolayer of macro-scopic granular particles lying on a vibrated surface and show that it provides a faithful realisation of active matter. The vibration feeds energy into the tilting vertical motion of the particles, which transduces it into a horizontal movement via frictional contact with the base in a direction determined by its orientation in the plane. We show that the dynamics of the particles can be easily controlled by manipulating their geometrical shapes. In the second part of the thesis, not addressing active matter, we do experiments on a soft condensed mat-ter system of viscoelastic surfactant gel formed of an entangled network of wormlike micelles and shows shear-thinning and is therefore non-Newtonian. These systems have relaxation times of the order of seconds and we have studied their non-equilibrium response properties when driven out of equilibrium externally by the gravitational sedimentation of objects and rising air-bubbles. Chapter 1 gives a general introduction to the term active matter and emphasize particularly on how these systems are internally driven and work far away from the equilibrium. We then explain in detail how a system of granular particles lying on a vibrating surface acts as active matter. We later give a brief introduction to the field of soft condensed matter and discuss the viscoelastic properties of surfactant solutions and their phase behaviour. We end this chapter by giving a brief introduction to flocking and non-equilibrium fluctuation relations which act as prerequisite to the following chapters. In Chapter 2 we discuss the experimental techniques used by us. We will first describe the shapes and dimensions of the granular particles used in the experiments. Next we introduce the shaker set-up and describe the experimental cell in which the particles are confined and variation in cell’s boundary. We show the dynamics of the particles in a quasi one-dimensional channel and then in two-dimensions. We give a brief account of image analysis and tracking algorithms employed and other data analyses techniques. In Chapter 3, we study the non-equilibrium fluctuations of a self-propelled polar particle moving through a background of non-motile spherical beads in the context of the Gallavotti-Cohen Fluctuation Relation (GCFR), which generalizes the second law of thermodynamics by quantifying the relative probabilities of the instantaneous events of entropy consumption and production. We find a fluctuation relation for a non-thermodynamic quantity, the velocity component along the long axis of the particle. We calculate the Large Deviation Function (LDF) of the velocity fluctuations and find the first experimental evidence for its theoretically predicted slope singularity at zero. We also propose an independent way to estimate the mean phase-space contraction rate. In Chapter 4 we expand the analysis done in Chapter 3 and study the two-dimensional velocity vector of the particle in the context of Isometric Fluctuation Relation (IFR) which measures the relative probability of current fluctuations in different directions in space of dimension >1. We first show that the dynamics of the particle is not isotropic and present a minimal model for its dynamics as a biased random walker, driven by a noise with anisotropic strength and construct an Anisotropic IFR (AIFR). We then show that the velocity statistics of the polar particle agree with the AIFR. We also confirm that the GCFR can be obtained as a special case of AIFR when the velocity vectors point in opposite directions. We calculate the LDF of particle’s velocity vector and find an extended kink in the velocity plane. In Chapter 5 we study the flocking phenomenon of a collection of polar particles when moving through a background of non-motile beads. We show that in the presence of bead medium, polar particles can flock at much lower concentrations, in contrast to the Vicsek model which predicts flocking at high concentrations. We show that the moving rods lead to a bead flow which in turn helps them to communicate their orientations and velocities at much greater distances. We provide a phase diagram in the parameter space of concentrations of beads and polar particles and show power-law spatial correlations as we approach the phase boundary. We also discuss the numerical simulations and theoretical model presented which support the experiments results. In Chapter 6 we experimentally study the angle dependence of the trapping of collection of active granular rods in a chevron shaped geometry. We show the particles undergo a trapping-detrapping transition at θ = 1150. On the contrary, this angle value is θ = 700 for a single rod. We find a substantial decrease in rotational noise for a collection of particles inside a trap as compared to a single rod which explains the increased value of θ for the trapping-detrapping transition. We also show that polar active particles which tend to change their direction of motion do not show the trapping phenomenon. In Chapter 7 we conduct experiments on falling balls and rising air bubbles through a non-Newtonian solution of surfactant CTAT in water, which forms a viscoelastic wormlike micellar gel. We show that the motion of the ball undergoes a transition from a steady state to oscillatory as the diameter of the ball is increased. The oscillations in velocity of the ball are non-sinusoidal, consisting of high-frequency bursts occurring periodically at intervals long compared to the period within the bursts. We present a theoretical model based on a slow relaxation mechanism owing to structural instabilities in the constituent micelles of the viscoelastic gel. For the case of air bubbles, we show that an air bubble rising in the viscoelastic gel shows a discontinuous jump in the velocity beyond a critical volume followed by a drastic change in its shape from a teardrop to almost spherical. We also observe shape oscillations for bigger bubbles with the tail swapping in and out periodically.

Τα κοκκώδη υλικά είναι αναπόσπαστο κομμάτι του κόσμου μέσα στον οποίο ζει ο άνθρωπος, και συνεπώς, για την καλύτερη κατανόηση του κόσμου αυτού, επιβάλλεται η μελέτη τους. Αυτός είναι και ο σκοπός της παρούσας διδακτορικής διατριβής. Επικεντρωνόμαστε σε διάδρομο μεταφοράς ο οποίος αποτελεί αντιπροσωπευτικό μοντέλο για πληθώρα εφαρμογών τόσο στην βιομηχανία όσο και στο φυσικό περιβάλλον. Αποτελεί επίσης χαρακτηριστικό παράδειγμα της οικογένειας ανοικτών πολυσωματιδιακών συστημάτων, η οποία βρίσκεται στην καρδιά της σύγχρονης επιστήμης της Πολυπλοκότητας. Αρχικά εισάγουμε το μοντέλο ροής στο οποίο το κοκκώδες υλικό αντιμετωπίζεται ως ένα ειδικό ρευστό (συνεχές μέσο) με εσωτερική απώλεια ενέργειας. Μελετάμε τη δυναμική ισορροπία που επικρατεί στο σύστημα υπό σταθερές συνθήκες, καθώς και την κατάρρευση της ομαλής ροής μέσω του σχηματισμού συσσωματώματος. Ειδική μνεία γίνεται στα πρόδρομα φαινόμενα της συσσωμάτωσης, τα οποία ερμηνεύουμε μέσω μίας αντίστροφης διακλάδωσης διπλασιασμού περιόδου. Διερευνώντας την εξάρτηση μεταξύ της μορφής της ροϊκής συνάρτησης και του τρόπου με τον οποίο το σύστημα μεταβαίνει σε καθεστώς συσσωμάτωσης αποκαλύπτουμε τόσο ποιοτικές όσο και ποσοτικές διαφορές σε σχέση με τον παραπάνω τύπο διακλάδωσης. Μια σημαντική παραλλαγή του συστήματος μεταφοράς προκύπτει εφαρμόζοντας ανατροφοδότηση του πρώτου δοχείου με το συνολικό υλικό που εκρέει από το τελευταίο. Η μαθηματική επεξεργασία αποδεικνύει ότι σε αυτήν την περίπτωση η δημιουργία συσσωματώματος συντελείται μέσω μιας διακλάδωσης Hopf αντί για διακλάδωσης διπλασιασμού περιόδου. Επιστρέφοντας στο αρχικό μας σύστημα, μελετάμε και το συνεχές όριο, θεωρώντας το διάδρομο μεταφοράς να έχει «άπειρο» μήκος. Η δυναμική ισορροπία, που ισοδυναμεί με το ισοζύγιο της μάζας ανάμεσα σε διαδοχικά δοχεία του διακριτού συστήματος, τώρα παίρνει τη μορφή μιας μη γραμμικής μερικής διαφορικής εξίσωσης δεύτερης τάξης με μη σταθερούς συντελεστές. Η προσεκτική μελέτη της εξίσωσης και των συντελεστών της, σε συνδυασμό πάντα με τις συνοριακές συνθήκες στην είσοδο και έξοδο του διαδρόμου, μας επιτρέπει όχι μόνο να αναπαραγάγουμε τα προηγούμενα αποτελέσματα υπό το πρίσμα του συνεχούς ορίου αλλά και να τα ερμηνεύσουμε βάσει φυσικών διεργασιών όπως είναι η μεταφορά (drift) και η διάχυση (diffusion). Ειδικότερα, η συσσωμάτωση συμβαίνει σε καθεστώς αρνητικής διάχυσης (antidiffusion). Κλείνουμε την διατριβή προτείνοντας γενικεύσεις των συστημάτων που ερευνήσαμε. Επεκτείνουμε το διάδρομο μεταφοράς σε πλέγματα δύο διαστάσεων και μελετάμε άλλα μοντέλα που σχετίζονται με ροές διακριτών σωματιδίων όπως είναι η κυκλοφορία οχημάτων στους αυτοκινητοδρόμους. / Granular materials are ubiquitous in nature and in our daily lives, and understanding their behavior is therefore of crucial importance. The present thesis wants to contribute to this. We focus on a conveyor belt, which is not only a representative model for numerous applications both in industry and the natural environment, but also a prime example of an open multi-particle system prone to spontaneous pattern formation. This places our study right in the center of the modern science of complexity. Initially we introduce the flux model, in which the granular material is treated as a special fluid (a continuous medium) with internal energy losses. We examine the dynamic equilibrium that exists in the system under steady state conditions and also the breakdown of this equilibrium when the inflow rate exceeds a certain critical threshold value, resulting in the formation of a cluster and the obstruction of the conveyor belt. We focus especially on the pre-clustering phenomena and find that these can be described mathematically by a reverse period doubling bifurcation. Investigating the relation between the precise form of the flux function and the way in which the transition to the clustered state takes place, we reveal that the above scenario via a reverse period doubling bifurcation is not universal. Also other bifurcation types are possible. An important variation of our transport system is obtained by applying a feedback mechanism: All the particles that flow out from the last compartment are inserted into the first, making the system closed with respect to matter (mass conservation). The mathematical analysis proves that in this case the cluster formation occurs via a Hopf bifurcation instead of a period doubling. Returning to our original system, we study its continuum limit by considering a conveyor belt of ‘infinite’ length. The dynamics of the system is now described by a second-order nonlinear partial differential equation with non-constant coefficients. A careful analysis of this PDE and its coefficients, in combination with the special boundary conditions at the entrance and exit of the system, allows us not only to reproduce the results of the discrete system in the setting of differential equations but also to interpret these results in terms of physical processes such as drift and diffusion. In particular, the clustering occurs when the diffusion coefficient becomes negative, which gives antidiffusion. We close this thesis by discussing several generalizations of the system investigated. Among other things we expand the one-dimensional conveyor belt to a two-dimensional lattice. We further propose to use a similar flux model for the study of other, non-granular instances of discrete particle flows, such as vehicles on a highway.