Universal shapes formed by two interacting cracks

We investigate the origins of the widely-observed "en passant" crack pattern which forms through interactions between two approaching cracks. A rectangular elastic plate is notched on each long side and then subjected to quasistatic uniaxial strain from the short side. The two cracks propagate along approximately straight paths until they pass each other, after which they curve and release a lenticular fragment. We find that for materials with diverse mechanical properties, the shape of this fragment has an aspect ratio of 2:1, with the length scale set by the initial crack offset $s$ and the time scale set by the ratio of $s$ to the pulling velocity. The cracks have a universal square root shape which we understand using a simple geometric model of the crack-crack interaction

Local origins of volume fraction fluctuations in dense granular materials

Fluctuations of the local volume fraction within granular materials have previously been observed to decrease as the system approaches jamming. We experimentally examine the role of boundary conditions and inter-particle friction $\mu$ on this relationship for a dense granular material of bidisperse particles driven under either constant volume or constant pressure. Using a radical Vorono\"i tessellation, we find the variance of the local volume fraction $\phi$ monotonically decreases as the system becomes more dense, independent of boundary condition and $\mu$. We examine the universality and origins of this trend using experiments and the recent granocentric model \cite{Clusel-2009-GMR,Corwin-2010-MRP}, modified to draw particle locations from an arbitrary distribution ${\cal P}(s)$ of neighbor distances $s$. The mean and variance of the observed ${\cal P}(s)$ are described by a single length scale controlled by $\bar \phi$. Through the granocentric model, we observe that diverse functional forms of ${\cal P}(s)$ all produce the trend of decreasing fluctuations, but only the experimentally-observed ${\cal P}(s)$ provides quantitative agreement with the measured $\phi$ fluctuations. Thus, we find that both ${\cal P}(s)$ and ${\cal P}(\phi)$ encode similar information about the ensemble of observed packings, and are connected to each other by the local granocentric model

La transition de "Jamming" dans un milieu granulaire bidimensionnel : Statique et dynamique d'un système athermique modèle

The Jamming transition is a generic phenomenon that occurs when an assembly abruptly ceases to evolve. This thesis proposes a characterization of the statistical properties of a model athermal system in the vicinity of this transition. The system, a bidimensionnal layer of 8500 metal cylinders, is studied in two experimental situations. The first one consists in examining the interstitial volume trapped in vertical packings of these grains. We show that in this static situation, the system exhibits long range correlations and a lack of extensivity. The second situation consists in vibrating such an assembly in the horizontal plane at various densities.We identify the Jamming transition on the force signal at the boundary.We study the diffusion properties together with the density field relaxation, and show that they both are governed by the same length scale.We then study the spatial heterogeneity of the dynamics by means of a four-point correlation function, which is found to verify critical scaling. The correlation length and a relaxation time scale associated with marginal super diffusion are maximum across the transition. We conclude that Jamming is a dynamical phase transition that nevertheless differs from the glass transition. Finally, our system is found to saturate a fluctuation dissipation inequality, which shows that the amplitude of spontaneous fluctuations of the dynamics is reproduced by its response to a change in density. We conclude that the latter governs the macroscopic properties of the system.La transition de Jamming est un phénomène générique qui se produit lorsqu'une assemblée d'objets cesse brusquement d'évoluer. Cette thèse propose une caractérisation des propriétés statistiques d'un système athermique modèle au voisinage de cette transition. Le système, une couche bidimensionnelle de 8500 cylindres métalliques, est étudié dans deux situations expérimentales. La première consiste à examiner le volume interstitiel piégé dans des empilements verticaux de ces grains. Nous montrons que dans cette situation statique, le système exhibe des corrélations à longue portée et un défaut d'extensivité. La seconde situation consiste à vibrer cette assemblée dans le plan horizontal à différentes densités. Nous identifions la transition de Jamming sur le signal de force à la paroi. Nous étudions les propriétés de diffusion et la relaxation du champ de densité, et montrons qu'une unique longueur caractéristique pilote ces deux quantités. Nous étudions ensuite l'hétérogénéité spatiale de la dynamique au moyen d'une fonction de corrélation à quatre points. Cette fonction vérifie une relation de scaling critique. A la transition, la longueur de corrélation ainsi qu'un temps de relaxation associé au phénomène marginal de super diffusion sont maximum. Nous en concluons que le blocage est une transition de phase dynamique, qui se distingue cependant de la transition vitreuse. Enfin, notre système sature une inégalité de fluctuation dissipation, ce qui nous permet de montrer que l'amplitude des fluctuations spontanées de la dynamique est bien reproduite par sa réponse à une variation de densité, et de conclure que cette dernière pilote les propriétés macroscopiques du système

Geometry and Elasticity of a Knitted Fabric

International audienceKnitting is not only a mere art and craft hobby but also a thousand-year-old technology. Unlike weaving, it can produce loose yet extremely stretchable fabrics with almost vanishing rigidity, a desirable property exhibited by hardly any bulk material. It also enables the engineering of arbitrarily shaped two- and threedimensional objects with tunable mechanical response. In contrast with the extensive body of related empirical knowledge and despite a growing industrial interest, the physical ingredients underlying these intriguing mechanical properties remain poorly understood. To make some progress in this direction, we study a model tricot made of a single elastic thread knitted into a common pattern called stockinette. On the one hand, we experimentally investigate its tensile response and measure local displacements of the stitches during deformation. On the other hand, we derive a first-principle mechanical model for the displacement field based on the yarn-bending energy, the conservation of its total length, and the topological constraintson the constitutive stitches. Our model solves both the shape and mechanical response of the knit andagrees quantitatively with our measurements. This study thus provides a fundamental framework for theunderstanding of knitted fabrics, paving the way to thread-based smart materials

Crackling Dynamics in the Mechanical Response of Knitted Fabrics

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Roughness of oxide glass sub-critical fracture surfaces.: How to measure and how to interpret?

International audienceAn original setup combining a very stable loading stage, an atomic force microscopy and an environmental chamber, allows to obtain very stable sub-critical fracture propagation in oxide glasses under controlled environment, and subsequently to finely characterize the nanometric roughness properties of the crack surfaces. In this presentation, I will focus, on one hand, on the special experimental care that has to be devoted to measure the metrological properties of such nanometric rough surface by Atomic Force Microscopy (AFM) and, on the other hand, on the interest of analyses in terms of physical indicators related to the self-affine nature of the fracture surfaces. Due to the comparable nanometric amplitude of the surface roughness, the AFM tip size and the instrumental noise, it seems interesting to discuss about potential experimental artefacts highlighted by Lechenault et al. The roughness amplitude of several oxide glasses was shown to decrease as a function of the stress intensity factor, to be quite insensitive to the relative humidity and to increase with the content of network modifiers . These results will be discussed in terms on several modellings concerning the coupling between crack propagation, material heterogeneity, crack tip plastic deformation and water diffusion at the crack tip taking into account the self-affine nature of the fracture surfaces

Experimental Evidence of Thermal-Like Behavior in Dense Granular Suspensions

International audienceWe experimentally investigate the statistical behavior of a model two-dimensional granular system undergoing stationary sedimentation. Buoyant cylindrical particles are rotated in a liquid-filled drum, thus confined in a harmonic centripetal potential with tunable curvature, which competes with gravity to produce various stationary states: though heterogeneous, the packing fraction of the system can be tuned from fully dispersed to crystallized as the rotation rate is increased. We show that this dynamical system is in mechanical equilibrium in the confining potential and exhibits a thermal-like behavior, where the granular pressure and the packing fraction are related through an equation of state. We obtain an expression of the equation of state allowing us to probe the nature of the hydrodynamic interactions between the particles. This description is valid in the whole range of the physical parameters we investigated and reveals a buoyant energy scale that we interpret as an effective temperature. We finally discuss the behavior of our system at high packing fractions and the relevance of the equation of state to the liquid-solid phase transition