Thermodynamics of Materials with Memory Theory and Applications
This is a work in four parts, dealing with the mechanics and thermodynamics of materials with memory, including properties of the dynamical equations which describe their evolution in time under varying loads. The first part is an introduction to Continuu
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Giovambattista Amendola Mauro Fabrizio John Murrough Golden
Thermodynamics of Materials with Memory Theory and Applications
Giovambattista Amendola Dipartimento di Matematica Applicata ‘‘U. Dini” University of Pisa via F. Bounarroti 1c 56127 Pisa Italy [email protected]
Mauro Fabrizio Dipartimento di Matematica University of Bologna Piazza di Porta S. Donato 5 40127 Bologna Italy [email protected]
John Murrough Golden Dublin Institute of Technology School of Mathematical Sciences Kevin Street Dublin 8 Ireland [email protected]
e-ISBN 978-1-4614-1692-0 ISBN 978-1-4614-1691-3 DOI 10.1007/978-1-4614-1692-0 Springer New York Dordrecht Heidelberg London Library of Congress Control Number: 2011940965 Mathematics Subject Classification (2010): 74A15, 74D05, 30E20, 35J10, 35K05
© Springer Science+Business Media, LLC 2012 All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)
Dedicated to Adele, Alessandra, and Marie
Preface
This book arose out of a conversation that took place in a bookshop in Berkeley, California, almost a decade ago. The original motivation was to provide a text on continuum thermodynamics that would allow a systematic derivation and discussion of free-energy functionals for materials with memory, including in particular explicit expressions for the minimum and related free energies, which were being developed at the time. Progress was very slow, due to other commitments. The vision of what the book would explore broadened considerably over the years, in particular to include minimal states and a new single-integral free-energy functional that explicitly depends on the minimal state. Also, it was decided to include a detailed description of an alternative approach to the analysis of the integrodifferential equations describing the evolution of viscoelastic materials under varying loads, using minimal states and free-energy functionals depending on the minimal state. This is a novel approach to a well-known topic. Our desire was to make the work as self-contained as possible, so chapters dealing with the general theory of continuum mechanics were included, with sections devoted to classical materials, specifically elastic bodies and fluids without explicit memory-dependence. These provided essential background to the more g
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