Shear Bands in Granular Materials: Formation and Persistence at Smooth Walls

This thesis contains numerical studies of rheology and shear characteristics of dense assemblies of granular materials. Beside the various experimental and theoretical studies, which deal with these materials, there is also a wide variety of simulation methods, which are used to study the flow behavior, compaction and other characteristics of granular materials. In this work, the contact dynamics method (CD) has been used to study two-dimensional systems of hard, dry disks. The particles interact by Coulomb friction forces parallel to, and volume exclusion forces normal to the contact surfaces, with collisions being fully inelastic. The shear flow is confined between two parallel, smooth, frictional walls, moving with opposite prescribed velocities. Discrete element simulations, carried out in samples with prescribed normal stress reveal that, unlike rough walls made of strands of particles, absolutely smooth but frictional ones can lead to inhomogeneous shear rate and shear strain localization in boundary layers. These are both caused by slip at smooth walls. Three shear regimes associated with different shear velocity intervals are identified and studied in this work. The transitions between these regimes are essentially independent of system size and occur for specific values of shear velocity. Applying constitutive laws deduced both for the bulk material and the boundary regions supplemented by an elementary stability analysis, the occurrence of both transitions, as well as the characteristic transient times are predicted. Investigating the role of the rotational degrees of freedom of round frictional particles and their microscopic contact properties at smooth walls, a critical microscopic friction coefficient at the walls is identified, below which the walls are unable to shear the system. New distinctive features are observed at this critical point. To perform a finite-size-analysis, simulations with very large systems have been frequently necessary during this thesis. To afford large scale simulations with CD, which are more comparable to real granular systems, within a conceivable time, a fully parallel version of CD is presented in this work. For large enough systems, 100% efficiency is achieved for up to 256 processors using a hierarchical domain decomposition with dynamic load balancing. Compared to the sequential implementation, no influence of the parallelization on simulation results is found.Scherbänder in granularer Materie: Entstehung und Stabilität an glatten Wänden Diese Arbeit behandelt die numerische Untersuchung der Rheologie und Schereigenschaften granularer Materie aus runden Teilchen. Neben den vielfältigen experimentellen und theoretischen Arbeiten, die sich mit dieser Materie beschäftigen, gibt es unterschiedliche Simulationsmethoden mit denen das Fließverhalten, die Kompaktierung und andere Eigenschaften granularer Materie untersucht werden. In dieser Arbeit wurde die Kontakt-Dynamik-Methode (CD) zur Untersuchung eines zweidimensionalen Systems aus granularer Materie angewandt. Die Teilchen sind starre Scheiben und die einzigen Kontaktkräfte zwischen diesen sind die Coulombsche Reibungskraft parallel und Volumenausschluss-Kräfte senkrecht zur Kontaktfläche. Die Teilchen befinden sich in einem System mit planarer Geometrie, das von oben und unten durch zwei parallele Wände begrenzt ist. Der Druck und die Schergeschwindigkeit sind in jeder Simulation fest vorgegeben und bleiben während der gesamten Simulation konstant. In dieser Arbeit werden, im Gegensatz zu vielen aktuellen Untersuchungen, absolut glatte, mit Reibung versehene Wände zur Scherung benutzt. Diese führen zu sehr inhomogenen Scherraten im System mit deutlicher Scherlokalisierung an den Wänden, die durch den Schlupf an diesen verursacht wird. Drei unterschiedliche Scherregime werden hierbei beobachtet. Jedes dieser Regime gehört zu einem wohldefinierten Intervall der Schergeschwindigkeit, das hauptsächlich von der Systemgröße unabhängig ist. Sowohl die Eigenschaften dieser drei Regime als auch die beiden Übergänge zwischen Ihnen werden detailliert in Kapitel 6 behandelt. In Kapitel 7 werden die konstitutiven Gesetze separat im Bulk und in den Grenzgebieten zu den Wänden hergeleitet. Anhand dieser konstitutiven Gesetze und ergänzender elementarer Stabilitätsanalysen wird das Vorkommen beider Übergänge, sowie charakteristische Transientenzeiten vorausberechnet. In Kapitel 8 wird eine kritische Mindestgröße des Reibungskoeffizienten an glatten Wänden festgestellt, die das Scheren ermöglicht. Bei diesem kritischen Reibungskoeffizienten wird ein besonderes Verhalten des Systems im quasistatischen Regime beobachtet, über welches zuvor noch nicht in der Literatur berichtet worden ist. In Kapitel 9 wird über eine erfolgreiche Parallelisierung der CD berichtet. Diese ermöglicht Simulationen in größeren Systemen, eher vergleichbar zur realen Systemen, die ebenso für die ``Finite-Size-Analyse'' notwendig sind

Novel Degrees of Freedom, Constraints, and Stiffness Formulation for Physically Based Animation

I identify and improve upon three distinct components of physically simulated systems with the aim of increasing both robustness and efficiency for the application of computer graphics: A) the degrees of freedom of a system; B) the constraints put on that system; C) and the stiffness that derives from force differentiation and in turn enables implicit integration techniques. These three components come up in many implementations of physics-based simulation in computer animation. From a combination of these components, I explore four novel ideas implemented and experimented on over the course of my graduate degree. Eulerian-on-Lagrangian Cloth Simulation resolves a longstanding problem of simulating contact-mediated interaction of cloth and sharp geometric features by exploring a combination of all three of our components. Bilateral Staggered Projections for Joints explores the constrained degrees of freedom of articulated rigid bodies in a reduced state to extend the popular Staggered Projects technique into a novel formulation for rapid evaluation of frictional articulated dynamics. Condensation Jacobian with Adaptivity looks at using reduction methods to improve the efficiency of soft body deformations by allowing larger time step in dynamics simulations. Finally, Ldot: Boosting Deformation Performance with Cholesky Extrapolation explores the inner workings of sparse direct solvers to introduce a Cholesky factorization that is linearly extrapolated in time, which can improve the performance when encapsulated inside an iterative nonlinear solver

Algorithmes de résolution de la dynamique du contact avec impact et frottement

The applications of the nonsmooth multibody systems field cover several fields including aeronautics, automotive, robotics, railway, virtual reality and watch industry to cite a few. These industrial applications have ever more stringent requirements on both accuracy and speed of the numerical methods used for the computation of the dynamics. As a consequence, the research in the nonsmooth mechanics domain is very active, to provide better integration methods for the resolution of the equations of motions and to develop better models for the contact problems with and without friction. Since the nonsmooth mechanics framework allows for jumps in the velocity and in the acceleration of the mechanical systems, the resulting algorithms have to handle such non-smoothness. In this PhD, several numerical schemes for the resolution of index-3, index-2 and index-1 DAEs are compared on industrial benchmarks with bilateral and unilateral constraints. The aim is to improve the efficiency of the Ansys Rigid Body solver which is based on an event-driven integration strategy. Points of comparison include the enforcement of the bilateral constraints, time efficiency and handling the stiff dynamics. This study also aimed at having a clear idea on the choice of the most suitable integration method for a given mechanical system knowing its characteristics (number of contacts, presence of bilateral constraints, stiff dynamics...). The second part discusses several issues that frequently occur in the simulation of multibody systems, namely, the problem of accumulation of impacts, the resolution of friction and handling the jumps resulting from the presence of some geometrical singularities. Dealing with such issues is very difficult, especially in the framework of event-driven schemes. In order to handle these problems, a mixed event-driven/time-stepping scheme is developed which takes advantage of both integration families (event-driven and time-stepping). Several examples are used to validate our methodology.La simulation des systèmes multicorps avec une dynamique non régulière trouve ses applications dans différents domaines comme l'aéronautique, l'automobile, le ferroviaire, la robotique, la réalité virtuelle et même l'industrie horlogère. Ces industries ont de plus en plus d'exigences sur la rapidité ainsi que la précision des méthodes utilisées pour calculer la dynamique. Par conséquent, la recherche dans le domaine de la mécanique non régulière est très active et a pour objectif constant de proposer des algorithmes plus robustes et plus rapides pour calculer la dynamique ainsi que de développer de meilleurs modèles pour le contact avec ou sans frottement. Les méthodes proposées doivent en plus bien gérer les sauts dans la vitesse et l'accélération des systèmes, ces sauts résultent de phénomènes tels que l'impact et le frottement. Dans ce manuscrit, quelques méthodes d'intégration d'équations différentielles algébriques d'index 3, 2 et 1 sont testées sur plusieurs mécanismes industriels avec contraintes unilatérales et bilatérales. Ces méthodes sont ensuite comparées sur la base de la satisfaction des contraintes bilatérales, de l'efficacité numérique et de leur capacité à gérer une dynamique raide. Cette étude a aussi permis d'apporter une réponse claire sur le choix de la méthode d'intégration pour un système mécanique connaissant ses caractéristiques (nombre de contacts, présence de contraintes bilatérales, dynamique raide...). La deuxième partie de ce travail traite certains problèmes qui sont fréquemment rencontrés dans la simulation des systèmes multicorps, notamment: le phénomène d'accumulation des impacts, la résolution du frottement, ainsi que la gestion des sauts qui peuvent être provoqués par la présence de singularités géométriques. Calculer la dynamique dans ces cas est particulièrement difficile dans le cadre des schémas event-driven. La solution proposée est un schéma d'intégration mixte "event-driven/time-stepping" dont le but est d'utiliser les avantages de chacune des familles d'intégration (event-driven et time-stepping). Notre algorithme est ensuite testé sur de nombreux exemples

Algorithmes de résolution de la dynamique du contact avec impact et frottement

The applications of the nonsmooth multibody systems field cover several fields including aeronautics, automotive, robotics, railway, virtual reality and watch industry to cite a few. These industrial applications have ever more stringent requirements on both accuracy and speed of the numerical methods used for the computation of the dynamics. As a consequence, the research in the nonsmooth mechanics domain is very active, to provide better integration methods for the resolution of the equations of motions and to develop better models for the contact problems with and without friction. Since the nonsmooth mechanics framework allows for jumps in the velocity and in the acceleration of the mechanical systems, the resulting algorithms have to handle such non-smoothness. In this PhD, several numerical schemes for the resolution of index-3, index-2 and index-1 DAEs are compared on industrial benchmarks with bilateral and unilateral constraints. The aim is to improve the efficiency of the Ansys Rigid Body solver which is based on an event-driven integration strategy. Points of comparison include the enforcement of the bilateral constraints, time efficiency and handling the stiff dynamics. This study also aimed at having a clear idea on the choice of the most suitable integration method for a given mechanical system knowing its characteristics (number of contacts, presence of bilateral constraints, stiff dynamics...). The second part discusses several issues that frequently occur in the simulation of multibody systems, namely, the problem of accumulation of impacts, the resolution of friction and handling the jumps resulting from the presence of some geometrical singularities. Dealing with such issues is very difficult, especially in the framework of event-driven schemes. In order to handle these problems, a mixed event-driven/time-stepping scheme is developed which takes advantage of both integration families (event-driven and time-stepping). Several examples are used to validate our methodology.La simulation des systèmes multicorps avec une dynamique non régulière trouve ses applications dans différents domaines comme l'aéronautique, l'automobile, le ferroviaire, la robotique, la réalité virtuelle et même l'industrie horlogère. Ces industries ont de plus en plus d'exigences sur la rapidité ainsi que la précision des méthodes utilisées pour calculer la dynamique. Par conséquent, la recherche dans le domaine de la mécanique non régulière est très active et a pour objectif constant de proposer des algorithmes plus robustes et plus rapides pour calculer la dynamique ainsi que de développer de meilleurs modèles pour le contact avec ou sans frottement. Les méthodes proposées doivent en plus bien gérer les sauts dans la vitesse et l'accélération des systèmes, ces sauts résultent de phénomènes tels que l'impact et le frottement. Dans ce manuscrit, quelques méthodes d'intégration d'équations différentielles algébriques d'index 3, 2 et 1 sont testées sur plusieurs mécanismes industriels avec contraintes unilatérales et bilatérales. Ces méthodes sont ensuite comparées sur la base de la satisfaction des contraintes bilatérales, de l'efficacité numérique et de leur capacité à gérer une dynamique raide. Cette étude a aussi permis d'apporter une réponse claire sur le choix de la méthode d'intégration pour un système mécanique connaissant ses caractéristiques (nombre de contacts, présence de contraintes bilatérales, dynamique raide...). La deuxième partie de ce travail traite certains problèmes qui sont fréquemment rencontrés dans la simulation des systèmes multicorps, notamment: le phénomène d'accumulation des impacts, la résolution du frottement, ainsi que la gestion des sauts qui peuvent être provoqués par la présence de singularités géométriques. Calculer la dynamique dans ces cas est particulièrement difficile dans le cadre des schémas event-driven. La solution proposée est un schéma d'intégration mixte "event-driven/time-stepping" dont le but est d'utiliser les avantages de chacune des familles d'intégration (event-driven et time-stepping). Notre algorithme est ensuite testé sur de nombreux exemples

Dynamics Of Reconfigurable Multibody Space Systems Connected By Magnetic Flux Pinning

Many future space systems, from solar power collection satellites to sparseaperture telescopes, will involve large-scale space structures which must be launched in a modular fashion. Currently, assembling modular structures in orbit is a challenging problem in multi-vehicle control or human-vehicle interaction. Some novel approaches to assembling modular space structures or formation-flying space systems involve augmenting the system dynamics with non-contacting force fields such as electromagnetic interactions. However, familiar divergenceless forces are subject to Earnshaw's Theorem and require active control in 6 DOF for stability. This study proposes an approach to modular spacecraft assembly based on the passively stable physics of magnetic flux pinning, an interaction between superconductors and magnetic fields which is not limited by Earnshaw's Theorem. Spacecraft modules linked by flux pinning passively fall into stable, many-degree-of-freedom basins of attraction in which flux pinning holds the modules together with stiffness and damping but no mechanical contact. This dissertation reports several system identification experiments that characterize the physical properties of flux pinning for spacecraft applications and identify avenues for design of flux-pinning space hardware. Once assembled in orbit, altering a spacecraft to effect repairs or adapt to new missions presents significant control challenges as well. Flux-pinning technology also offers exciting possibilities for new spacecraft-reconfiguration techniques, in which a spacecraft changes structure and function at the system level. Flux-pinned modular spacecraft can reconfigure in such a way that the passive physics of flux pinning and the space environment govern the low-level dynamics of a reconfiguration maneuver, instead of full-state feedback control. These reconfiguration maneuvers take the form of sequences of passively stable evolutions to equilibrium states, with joint kinematics between modules preventing collisions. This dissertation develops a theory for multibody spacecraft reconfiguration controllers that take a high-level, hybrid-systems approach in which a pre-computed graph structure stores all the reachable configurations that meet certain design-specified criteria. Edges of the graph carry mission-related weights so that a space system can optimize power consumption, robustness measures, or other performance metrics during a maneuver. These technologies and control strategies may provide opportunities for versatile space systems that can accomplish a wide variety of future missions