Fractals and Randomness in Mechanics of Materials
These notes provide an introduction to two aspects of mechanics of materials: (i) effects of randomness on scaling to effective constitutive responses and (ii) fractal geometries. The first aspect is relevant when the separation of scales does not hold [i
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Tomasz Sadowski Patrizia Trovalusci Editors
Multiscale Modeling of Complex Materials Phenomenological, Theoretical and Computational Aspects
International Centre for Mechanical Sciences
CISM Courses and Lectures
Series Editors: The Rectors Friedrich Pfeiffer - Munich Franz G. Rammerstorfer - Wien Elisabeth Guazzelli - Marseille The Secretary General Bernhard SchreÁer - Padua Executive Editor Paolo SeraÀni - Udine
The series presents lecture notes, monographs, edited works and proceedings in the Àeld of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientiÀc and technical community results obtained in some of the activities organized by CISM, the International Centre for Mechanical Sciences.
International Centre for Mechanical Sciences Courses and Lectures Vol. 556
For further volumes: www.springer.com/series/76
Tomasz Sadowski · Patrizia Trovalusci Editors
Multiscale Modeling of Complex Materials Phenomenological, Theoretical and Computational Aspects
Editors Tomasz Sadowski Lublin University of Technology, Poland Patrizia Trovalusci “Sapienza” University of Rome, Italy
ISSN 0254-1971 ISBN 978-3-7091-1811-5 ISBN 978-3-7091-1812-2 (eBook) DOI 10.1007/ 978-3-7091-1812-2 Springer Wien Heidelberg New York Dordrecht London © CISM, Udine 2014 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, speciÀcally the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microÀlms 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 speciÀcally 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 speciÀc 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 contai
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