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4.2 Angular Velocity Research Collection Doctoral Thesis Non-Smooth Granular Rigid Body Dynamics with Applications to Chute Flows Author(s): Nützi, Gabriel Publication Date: 2016 Permanent Link: https://doi.org/10.3929/ethz-a-010662262 Rights / License: In Copyright - Non-Commercial Use Permitted This page was generated automatically upon download from the ETH Zurich Research Collection. For more information please consult the Terms of use. ETH Library Diss. ETH No. 23383 Non-Smooth Granular Rigid Body Dynamics with Applications to Chute Flows A thesis submitted to attain the degree of Doctor of Sciences of ETH Zurich (Dr. sc. ETH Zurich) presented by Gabriel Elias Nützi MSc ETH ME, ETH Zurich born on 31.10.1986 citizen of Wolfwil SO Switzerland accepted on the recommendation of Prof. Dr.-Ing. Dr.-Ing. habil. Christoph Glocker, examiner Prof. Dr.-Ing. Jürg Dual, co-examiner Prof. Dr. ir. habil. Remco I. Leine, co-examiner 2016 template<typename My> void to(My && family); Acknowledgement The work presented in this thesis has been carried out at the Institute for Mechanical Systems at the ETH Zurich. During these turbulent 4 years, I have been accompanied by many people whom I would like to devote my utmost thanks. At first place, I would like to thank my supervisor Prof. Dr.-Ing. Dr.-Ing. habil. Ch. Glocker for supporting my research during these four years. He has given me the unconditional opportunity to extend my curiosity and my interest in mechanics as well as to delve deep into the beauty and madness of computer science. I was very much impressed right from the start of my studies about his endeavor for effective teaching and his strong believe in an environment where prosperous research and well-structured and concise education shake hand. As a mentor he taught me that nothing is too simple to be treated as obvious and his minimal non-trivial mechanical examples became the archetypical examples in this matter. I also devote my gratitude to his meticulous style of technical drawings and notation – the literature in engineering science will be so much more understandable if more attention to this matter is given. As an assistant, I was very much pleased to contribute to the teaching of mechanics under his lead. Further thanks go to Prof. Dr.-Ing. Jürg Dual for his friendly welcome in his group and for his straightforward agreement to be my first co-examinator. Furthermore, I very much like to thank Prof. Dr. ir. habil. Remco Leine for serving as my second co-examiner even at hardship. He has helped me closing some gaps in understanding essential concepts in non-smooth mechanics and has confronted me with the right questions at the right time and has always lent an ear for technical and non- technical issues. I also want to thank Adrian Schweizer for sharing my office and for the fruitful technical and non-technical discussions and his patient willingness to teach me crazy stuff at the white board. I am also very thankful to Simon Eugster who helped me a lot in grasping some difficult concepts of modern continuum dynamics and for his continuous support throughout these four years. In this sense, I am also very thankful for Michael Baumann. His sharp-witted mathematical approach and his patience for my sometimes nonsense palaver was very much supportive. Playing chess together was much of a fun I already miss. Heartfelt thanks also go to the following people which supported and tolerated me in various ways: Michael Blösch, Raoul Hopf, George Rempfler, Thomas Heimsch. I am also thankful to Michael Möller for his profound advice and knowledge in computer science and to Ondrej Papes for the discussion about variational integrators. Further thanks go to Thierry Baasch for his efforts in GPU computing during his master thesis. Many thanks also to all the members of the group of Prof. Jürg Dual who made my work life and launch times very enjoyable. i ii Another special thank goes to Claudia Bieler, Tom Feistel, Silvio Bamert and Perry Bartelt without whom I would not have been able to carry out the chute flow experi- ments. I am also thankful to Xylar Asay-Davis who helped me in using his fancy correla- tion algorithm for my research. Many thanks also go to all the people of the open-source community at stackoverflow.com which answered countless questions during my re- search and to Urban Borštnik and the Euler/Brutus cluster support team at the ETH Zurich. I owe my deepest gratitude to Nadia Zollinger. I could not be more intimately grateful for her unconditional, selfless support, warmth and love. She always stood to my side even in unbearable times and has always been believing in me. Countless times she has been a patient listener not only to my many technical programming problems during this research. She will always stay my desirable reference when it comes to “treat others as you would wish to be treated”. I also thank Samuel Kilcher, Martin Knobel and Olaf Metzger for unforgettable climbing memories in Switzerland and abroad. I thank my family and my friends for the always moral support and continuous encour- agement. Without them, this work would not have been possible. Zurich, February 2016 Gabriel Elias Nützi Abstract The work presented in this monograph is a contribution to the field of granular rigid body dynamics and its related subfields in computer science. The main contribution of this work is an open-source granular rigid body simulation framework (GRSF) which incorporates modern formulations and algorithms within the framework of non-smooth rigid body dynamics to efficiently simulate granular materials. This work discusses gran- ular simulations in the context of their mechanical theory, their computer science related challenges and applications to real experiments. In this work, a granular material is treated on the microscopic space scale where the par- ticle interactions are treated as individual events over time. This modeling paradigm is of special interest because it gives detailed insight into the rheology and impacting behavior of granular materials in contrary to macroscopic models from fluid or continuum dynam- ics. The increasing trend in parallel computing at the present point in time evermore offers the performance needed to compute granular simulations also for large-scale mod- els. The granular material model adopted in this work consists of a large-scale rigid body assembly in the physical space. The time evolution of a body in space is driven by two fundamental axioms in mechanics: the principle of virtual work and the variational law of interaction. These two axioms are exploited to properly derive the equations of motion of a rigid body starting from a scalable body which is parametrized by a quaternion. Dissipation phenomena such as friction and impacts and the impenetrability condition between bodies in a granular material are conveniently modeled by set-valued contact laws. Concepts from convex analysis and convex optimization, such as normal cones and projections to convex sets, are directly at hand to describe and solve common set-valued contact laws, such as the unilateral contact with Coulomb friction. The contact laws are complemented with a Newton-type impact law to allow for discontinuities in the velocities of the bodies. The numerical time integration is performed with Moreau’s explicit time- stepping scheme which discretizes the continuous and discontinuous motion of the bodies over a time interval and provides a good trade-off between accuracy and efficiency for large-scale multi-body simulations. The aforementioned modern mechanical modeling aspects are implemented in the GRS framework which is able to efficiently and accurately simulate hundred thousands up to millions of rigid bodies. The parallel implementation, which mainly targets high- performance distributed systems, makes use of the mass-splitting method which subdi- vides the contact problem at each time step of the integration scheme. The contact problem, consisting of millions of contacts, is solved using iterative projection algorithms which are closely related to the methods from convex optimization. To spatially distribute the workload of the simulation, namely the time-stepping of the rigid bodies, to several processes, domain decomposition methods such as the grid or kd-tree decomposition are iii iv implemented in the GRS framework by the help of the open-source library ApproxMVBB which was developed alongside the GRS framework. A simple load balancing strategy is employed to leverage the parallel computing power for simulations where bodies rapidly distribute over time. The Message Passing Interface (MPI) is used to provide the com- munication interface on distributed systems and to communicate and synchronize the numerical computations during the parallel simulation. To demonstrate the functional ability of the GRS framework and to validate the numer- ical implementation, a chute flow experiment is performed at the institute of Snow and Avalanche Research (SLF) in Davos, Switzerland. The chute flow experiment consists of approximately 1 million glass beads which are released from rest in a channel above an inclined slope. A simulation study is performed where the friction coefficient between the glass beads is varied. By the help of an advection-corrected image correlation algorithm, the velocity field of the chute experiment is reconstructed and compared to the simulation. Visualizations ranging from two-dimensional velocity field plots to three-dimensional ren- derings provide meaningful insight into the results of the simulation and experiments. The comparison between the simulations and the experiment confirm the validity and usefulness of the numerical model implemented in the GRS framework. Zusammenfassung Die in der vorliegenden Abhandlung beschriebene Arbeit liefert einen Beitrag an die For- schung im Bereich der granularen Starrkörperdynamik und deren verwandten Unterbe- reichen der Computerwissenschaft. Der Hauptschwerpunkt der Arbeit liegt in der Umset- zung von modernen mechanischen Formulierungen im Bereich der nichtglatten Dynamik an Hand einer numerischen Softwareumgebung namens Granular Rigid Body Simulation Framework (GRSF), welche es erlaubt granulare Medien zu simulieren und zu untersu- chen.
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