Mechanics of Generalized Continua
This collection on „Mechanics of Generalized Continua - from Micromechanical Basics to Engineering Applications“ brings together leading scientists in this field from France, Russian Federation, and Germany. The attention in this publication is be focusse
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Series Editors Andreas Öchsner, Technical University of Malaysia, Skudai, Johor, Malaysia Lucas Filipe Martins da Silva, University of Porto, Porto, Portugal Holm Altenbach, University of Halle-Wittenberg, Halle, Germany
For further volumes: http://www.springer.com/series/8611
Holm Altenbach Gérard A. Maugin Vladimir Erofeev •
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Editors
Mechanics of Generalized Continua
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Editors Holm Altenbach Zentrum für Ingenieurwissenschaften Martin-Luther-Universität Halle-Wittenberg Kurt-Mothe-Str. 1 06099 Halle (Saale) Germany e-mail: [email protected]
Vladimir Erofeev IMASH, RAN Belinskogo str. 85 603024 Nizhny Novgorod Russia
Gérard A. Maugin Institut Jean Le Rond d’Alembert UPMC Tour 55, Place Jussieu 4 75252 Paris France
ISSN 1869-8433
e-ISSN 1869-8441
ISBN 978-3-642-19218-0
e-ISBN 978-3-642-19219-7
DOI 10.1007/978-3-642-19219-7 Springer Heidelberg Dordrecht London New York Ó Springer-Verlag Berlin Heidelberg 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable to prosecution under the German Copyright Law. The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Cover design: WMXDesign GmbH, Heidelberg Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Preface
Generalized Continua are in the focus of scientists from the end of the 19th century. A first summary was given in 1909 by the Cosserat brothers1 and some previous works of such famous scientists like Lord Kelvin. All these contributions were focussed on the fact that in a continuum one has to define translations and rotations independently (or in other words, one has to establish force and moment actions as it was done by Euler). After World War II a true renaissance in this field occurred with a publication of Ericksen & Truesdell in 1958. Further developments were connected with the fundamental contributions of, among others, Kr¨oner (Germany), Aero and Palmov (Soviet Union), Nowacki (Poland), Eringen (USA), and Maugin (France). The reason for the revival was that some effects of the mechanical behavior of solids and fluids could not be explained by the available classical models. Examples of this are the turbulence of a fluid or the behavior of solids with a significant and very complex microstructure. The enthusiasm in this field was so great that the International Union of Theoretical and App
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