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Mechanics and Thermodynamics of Mixtures with Continuous Diversity from Complex Media to Ice Sheets

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Mechanics and Thermodynamics of Mixtures with Continuous Diversity from Complex Media to Ice Sheets Mechanics and Thermodynamics of Mixtures with Continuous Diversity From Complex Media to Ice Sheets Vom Fachbereich Mechanik der Technischen Universit¨at Darmstadt zur Erlangung des akademischen Grades eines Doktors der Naturwissenschaften (Dr. rer. nat.) genehmigte Dissertation vorgelegt von S´ergio Henrique Faria Santos,M.Sc. aus Curitiba, Brasilien Referent: Prof. K. Hutter, Ph.D. Korreferent: Prof. Dr. rer. nat. G. M. Kremer Tag der Einreichung: 20. Dezember 2002 Tag der mundlichen¨ Prufung:¨ 5. M¨arz 2003 D17 To my dear Gis Acknowledgements This dissertation is the fruit of Prof. K. Hutter’s suggestion – better saying: chal- lenge – to develop a thermodynamic theory for polycrystalline ice sheets undergoing recrystallization. The emergence of the thermodynamic theory of mixtures with con- tinuous diversity and its subsequent applications to other complex media followed as an unanticipated (yet extremely pleasing) consequence. Much more than just for this prolific suggestion, I am sincerely grateful to him for his continuous motivati- on and interest in my work and professional development. The opportunities which he has offered to me during the last four years have been far beyond the greatest expectations, turning my work in Darmstadt extremely stimulating. There is no need to say how grateful I am to Prof. G.M. Kremer: he crossed the Atlantic, interrupting important research and teaching activities, just to be the co-referee of this dissertation. His respect for my work, as well as his passion for scientific discussions, have been a ceaseless source of inspiration to me during the last months. Further, I thank also Prof. D. Gross, Prof. W. Hauger and Prof. Ch. Tsakmakis for their kind acceptance to take part in the examination board. A special thank goes also to Prof. W.F. Muller¨ (TUD–Dept. of Geosciences) for his cordial presence at my Ph.D. exam. Within the Department of Mechanics, I want to express my gratitude to the professors and colleagues of all the four research groups, who have always cared for a good atmosphere of work. In particular, the distressing pressure of the academic bureaucracy has regularly been softened by the humane mastery of Ms. R. Rutscher and Ms. M. Geiger (formerly also of Ms. R. Danner), to whom I am deeply grateful. Concerning the members of my research group (AG3), I would really like to express my gratitude to them one by one – and not only to my present colleagues, but also to the former ones – but they are so many (and there is so much to acknowledge) that some extra pages would be needed. Thus, I must unfortunately restrict myself to a general, but very sincere, “thank you all”. Of course, there are some names which cannot be omitted. From the actual mem- bers of the group, I must mention my roommate, the super-mother Angelika Hum- bert (from whom I learned the importance of data analysis), my room-neighbor Dr. Harald Ehrentraut (who introduced me to the secrets of irreducible tensors), Dr. Yongqi Wang (who acquainted me with the fundamentals of granular media) and my “successor” Luca Placidi (who will make the theory of continuous diversity fly above and beyond its limits). From the former members of the group, there are some who became closer friends of mine, deserving thence special mention. Firstly, there is the memorable “life philosopher”, Dr. Alexander “Sasha” Wilchinsky (presently at the CPOM–University College of London), who is always optimistic when I am pessimistic and cheerfully “pessimistic” when I am in a happy mood. Talking about cheerfulness, it is impossible to avoid mentioning my former roommate Dr. Lars Um- lauf (presently at the Laboratoire d’Hydraulique Environnementale in Lausanne), a rich blend of scientist, artist and engineer, who convinced me that some Germans can also have that Latin “something else” (including eccentric blue shoes). Then, there is also Dr. Dimitri Ktitarev (presently at DB Systems GmbH), with whom I spent X some stressing weekends preparing “fabric diagrams” for a glaciology symposium in Greenland. Finally, I must express my gratitude to the first close friend I made in Darmstadt, Dr. Yih-Chin Tai (now at TUV in Taiwan), who surprised me with his presence at my Ph.D. examination. But there could be no complete acknowledgement without mentioning my love- ly friends Drs. Nina and Eckhard Kirchner (now at TU Kaiserslautern and Adam Opel AG, respectively). Nina was my first roommate and looked after me in a time when I could hardly understand German. She and her husband have indeed a deep comprehension of the difficulties encountered by anyone in a foreign country, and from them I learned a lot of useful things, from abrasion in granular matter to the preparation of creative wedding pictures. Outside the walls of TU Darmstadt I have also had the fortune of meeting good people who promoted a very positive influence upon my work. In particular, there are three persons to whom I am specially grateful: the first is Prof. G.K.C. Clarke (University of British Columbia), once called“one of the heroes of glaciology”(during a talk at the British Antarctic Survey), actually one of the kindest scientists I ever met, who taught me iceberg dynamics and made all efforts to turn my one-week stay in Cambridge an unforgettable experience. The second is Dr. J. Kipfstuhl (Alfred Wegener Institute Bremerhaven), whose affability – which is comparable only to his scientific curiosity – has made me regard him since the first sight not only as a colleague, but a friend. Finally, the third one is Prof. R. Lancellotta (Politecnico di Torino), who organized together with his colleagues a spring school on the continuum description of granular materials at the Politecnico and gave me the opportunity to hold some lectures on the homogenization of granular media and the theory of mixtures with continuous diversity. Finally, as my friends should suspect, I could not finish these acknowledgements without expressing my appreciation to the library of the TU Darmstadt (Landes- und Hochschulbibliothek Darmstadt) – a place where dreams come true. In fact, I will never forget the first time I read the originals of Cardano’s (1550) De Subtilitate [67] and Kepler’s (1611) Strena seu de nive sexangula [241]. In particular, I wish to thank the members of the efficient team of the lending service (“Ausleihe”), who measured no efforts to fulfill all my bibliographic necessities, which in fact went beyond the 437 works listed in the References. To tell the truth, I must confess that I could never manage to prepare such an unusually long list of references by myself: all the credits are to be given to my wife Gislaini Jacomini – she wrote all the items, while I was in a hurry to finish the text of the dissertation before Christmas (2002). I know that I should be ashamed for letting her doing such a hard work – specially if one recalls all the additional distresses to which Ph.D. students’ wives are inevitably subjected – and indeed I do so. More than this, she also read some parts of the dissertation draft, helping me to improve the English wording. And now that everything is finished, I still do not know how to thank her for everything she did for me during my Ph.D., including her love and support, except by saying “I love you” and dedicating all these four years of work to her. At last but not least, I want to thank all the kind persons who had no direct influence on this work, but gave me support through their friendship. In particular, XI I thank my family in Brazil – my dear mother Claudette, Rodrigo and Juliana, Maria Laudeceia and Valdir, Grasiani Cristina and Giuliana – for their love, assistance and care. This work was supported by a fellowship from the Coordena¸c˜ao de Aperfei- ¸coamento de Pessoal de N´ıvel Superior (CAPES) of Brazil. Abstract The aim of this thesis is to introduce to the reader the thermodynamic theory of mixtures with continuous diversity and to illustrate its potential through applications to diverse complex media. Chapter 1 offers a critical discussion about the intricacies in the description of com- plex media as continuous bodies. Fundamentals on the homogenization (structural averaging) of porous materials are presented in a concise way. Chapter 2 gives an up-to-date review of the homogenization of polar granular media, with emphasis on the peculiarities of its microstructure. Chapter 3 combines the concepts of homogenization, polar media and chemical mix- tures in a systematic manner, in order to derive appropriate balance equations for mixtures of microstructured media. Chapter 4 invokes the results of former chapters to resolve a contemporary polemic concerning energy invariance and inertial effects in chemically reacting mixtures of liquid crystals. Chapter 5 introduces the fundamental concepts of the thermodynamic theory of mixtures with continuous diversity from a generic perspective. Chapter 6 merges the formerly presented notions of microstructured media, chemi- cally reacting mixtures and mixtures with continuous diversity into the powerful theory of hybrid mixtures with continuous diversity, or “doubly complex” media. Chapter 7 employs the theory of mixtures with continuous diversity to study the microstructure evolution of polymeric solutions, more precisely suspensions of rigid rodlike macromolecules. Chapter 8 demonstrates how the texture evolution of polycrystalline media under- going recrystallization may be modeled by using the formalism of mixtures with continuous diversity. Besides a short historical synopsis of ice morphology research, the particular case of induced anisotropy and recrystallization in ice sheets is consi- dered. Chapter 9 concludes this work with an overview on future applications, specially on the modeling of iceberg ensemble dynamics during Heinrich events, as well as on the study of abrasion, fragmentation and particle size segregation in polydisperse granular media.
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