The Continuum Theory of Piezoelectricity and Piezomagnetism
Following the motivation of this work, this chapter introduces the basic concepts of continuum mechanics and electromagnetism. Attention is then focused on linear piezoelectricity, elaborating two ways of writing the governing equations: the displacement
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Anatoliy Malyarenko Martin Ostoja-Starzewski Amirhossein Amiri-Hezaveh
Random Fields of Piezoelectricity and Piezomagnetism Correlation Structures
SpringerBriefs in Applied Sciences and Technology Mathematical Methods
Series Editors Anna Marciniak-Czochra, Institute of Applied Mathematics, IWR, University of Heidelberg, Heidelberg, Germany Thomas Reichelt, Emmy-Noether Research Group, Universität Heidelberg, Heidelberg, Germany
More information about this subseries at http://www.springer.com/series/11219
Anatoliy Malyarenko Martin Ostoja-Starzewski Amirhossein Amiri-Hezaveh •
Random Fields of Piezoelectricity and Piezomagnetism Correlation Structures
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Anatoliy Malyarenko Division of Mathematics and Physics Mälardalen University Västerås, Sweden Amirhossein Amiri-Hezaveh Department of Mechanical Sciences and Engineering University of Illinois at Urbana-Champaign Urbana, IL, USA
Martin Ostoja-Starzewski Department of Mechanical Science and Engineering Institute for Condensed Matter Theory Beckman Institute University of Illinois at Urbana-Champaign Urbana, IL, USA
ISSN 2191-530X ISSN 2191-5318 (electronic) SpringerBriefs in Applied Sciences and Technology ISSN 2365-0826 ISSN 2365-0834 (electronic) SpringerBriefs in Mathematical Methods ISBN 978-3-030-60063-1 ISBN 978-3-030-60064-8 (eBook) https://doi.org/10.1007/978-3-030-60064-8 Mathematics Subject Classification: 00A69, 74Axx, 60G60 © The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 This work is subject to copyright. All rights are solely and exclusively licensed 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. 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. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, expressed or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Switzerland AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Preface
Spatially random materials pose mathematical challenges to theoretical physics and mechanics. These problems are exacerbated in the case of
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