Mathematical Modeling in Mechanics of Granular Materials
This monograph contains original results in the field of mathematical and numerical modeling of mechanical behavior of granular materials and materials with different strengths. It proposes new models helping to define zones of the strain localization. Th
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Series Editors Andreas Öchsner Lucas F. M. da Silva Holm Altenbach
For further volumes: http://www.springer.com/series/8611
Oxana Sadovskaya Vladimir Sadovskii •
Organized by Holm Altenbach
Mathematical Modeling in Mechanics of Granular Materials
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Vladimir Sadovskii ICM SB RAS Akademgorodok 50/44 Krasnoyarsk Russia 660036
Oxana Sadovskaya ICM SB RAS Akademgorodok 50/44 Krasnoyarsk Russia 660036 Holm Altenbach Magdeburg Germany
ISSN 1869-8433 ISBN 978-3-642-29052-7 DOI 10.1007/978-3-642-29053-4
ISSN 1869-8441 (electronic) ISBN 978-3-642-29053-4 (eBook)
Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012938145 Springer-Verlag Berlin Heidelberg 2012 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, 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. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Foreword
The new monograph ‘‘Mathematical Modeling in Mechanics of Granular Materials’’ written by Oxana & Vladimir Sadovskii is based on a previous Russian version published in 2008. The Russian version was significantly revised and extended. The References were updated with respect to the readers not being familiar with the Russian language. Instead of eight chapters of the Russian original version there are now ten chapters—a new chapter devoted to continua with independent rotational degrees of freedom is added. Lookin
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