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Publication# Jamming in granular media

Abstract

This thesis studies the phenomenon of jamming in granular media, such as when a salt shaker gets clogged. We use modern instrumentation, like X-ray synchrotron tomography, to look inside real jamming experiments. High performance computers allow simulating mathematical models of jamming, but we are also able to treat some of them just using paper and pencil. One main part of this thesis consists of an experimental validation of the distinct-element-method (DEM). In this model, grains are modeled separately, their trajectories obey Newton's laws of motion and a model of the contacts between grains is given. Real experiments of jamming of glass beads flowing out of a container were carried out. 3D snapshots of the interior of the media were taken using X-ray synchrotron tomography. These snapshots were computer processed using state of the art image analysis. It was found that 3D DEM is capable of predicting quite well the final positions of the grains of the real experiments. Indeed, in cases of instant jamming (jamming without a substantial previous flow of beads) the simulations agree well with the real experiments. However, in cases of non instant jamming, because of chaotic behavior of the model and the system, the results do not agree. Furthermore, a sensitivity analysis to grain location and size perturbations was carried out. In a second part, we describe results on 2D DEM simulations of jamming in a hopper. We focus on the jamming probability J, the average time T before jamming and the average number ψ of beads falling through the hole when jamming occurs. These quantities were related to global parameters such as the number of grains, the hole size, the friction coefficient, grain length or the angle of the hopper (in opposition to fine-scale parameters that are the positions and radii of the grains). In agreement with intuition, a monotonic behavior of J and ψ as a function of the number of grains, the hole size, the friction coefficient was found. However, surprising results were also found such as the non-monotonicity of the average number of beads falling through the hole when jamming occurs as a function of the grain length and the hopper angle. In the third part, we study simple probabilistic 2D models called SPM, in which non-interacting particles move with constant speed towards the center of a circular sector. Formulas giving the jamming probability or the average time before jamming when jamming occurs as a function of global parameters were found. SPM and 2D DEM were compared and a locally good correspondence between the global parameters of the two was established. SPM led us to study some combinatorial problems, in particular two bi-indexed recurrence sequences. One gives the number of ways of placing identical balls in fixed-size numbered urns and the other the number of subsets of a given ordered set without a certain number of consecutive elements. Several different ways of computing the sequences, each advantageous in certain cases, were found.

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Tiziano Leidi, Alberto Ortona, Jean-Philippe Thiran

In recent decades, finite element (FE) techniques have been extensively used for predicting effective properties of random heterogeneous materials. In the case of very complex microstructures, the choice of numerical methods for the solution of this problem can offer some advantages over classical analytical approaches, and it allows the use of digital images obtained from real material samples (e.g., using computed tomography). On the other hand, having a large number of elements is often necessary for properly describing complex microstructures, ultimately leading to extremely time-consuming computations and high memory requirements. With the final objective of reducing these limitations, we improved an existing freely available FE code for the computation of effective conductivity (electrical and thermal) of microstructure digital models. To allow execution on hardware combining multi-core CPUs and a CPU, we first translated the original algorithm from Fortran to C, and we subdivided it into software components. Then, we enhanced the C version of the algorithm for parallel processing with heterogeneous processors. With the goal of maximizing the obtained performances and limiting resource consumption, we utilized a software architecture based on stream processing, event-driven scheduling, and dynamic load balancing. The parallel processing version of the algorithm has been validated using a simple microstructure consisting of a single sphere located at the centre of a cubic box, yielding consistent results. Finally, the code was used for the calculation of the effective thermal conductivity of a digital model of a real sample (a ceramic foam obtained using X-ray computed tomography). On a computer equipped with dual hexa-core Intel Xeon X5670 processors and an NVIDIA Tesla C2050, the parallel application version features near to linear speed-up progression when using only the CPU cores. It executes more than 20 times faster when additionally using the CPU. (C) 2012 Elsevier B.V. All rights reserved.

Vincent Gajdosik, Thomas Liebling, Giorgio Margaritondo, Slobodan Mitrovic, Lionel Pournin, Marco Ramaioli, Daniel Sage, Michel Tsukahara, Michaël Unser

We describe an approach for exploring microscopic properties of granular media that couples x-ray microtomography and distinct-element-method (DEM) simulations through image analysis. We illustrate it via the study of the intriguing phenomenon of instant arching in an hourglass (in our case a cylinder filled with a polydisperse mixture of glass beads that has a small circular shutter in the bottom). X-ray tomography provides three-dimensional snapshots of the microscopic conditions of the system both prior to opening the shutter, and thereafter, once jamming is completed. The process time in between is bridged using DEM simulation, which settles to positions in remarkably good agreement with the x-ray images. Specifically designed image analysis procedures accurately extract the geometrical information, i.e., the positions and sizes of the beads, from the raw x-ray tomographs, and compress the data representation from initially 5 gigabytes to a few tens of kilobytes per tomograph. The scope of the approach is explored through a sensitivity analysis to input data perturbations in both bead sizes and positions. We establish that accuracy of size—much more than position—estimates is critical, thus explaining the difficulty in considering a mixture of beads of different sizes. We further point to limits in the replication ability of granular flows away from equilibrium; i.e., the difficulty of numerically reproducing chaotic motion.