Statistical Continuum Mechanics
In these sections we outline some basic ideas underlying the solution of statistical problems in conductivity, acoustics and elasticity. The problems we consider are both static and dynamic and the statistical nature of the problems sterns from the fact t
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Series Editors: The Rectors - Budapest Kaliszky Sandor Mahir Sayir - Zurich Wilhelm Schneider - Wien The Secretary General Bernhard Schrefler - Padua Former Secretary General Giovanni Bianchi - Milan Executive Editor Carlo Tasso - Udine
The series presents lecture notes, monographs, edited works and proceedings in the field of Mechanics, Engineering, Computer Science and Applied Mathematics. Purpose of the series is to make known in the international scientific 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 - No. 430
MECHANICS OF RANDOM AND MULTISCALE MICROSTRUCTURES
EDITED BY DOMINIQUE JEULIN ECOLE DES MINES DE PARIS MARTIN OSTOJA-STARZEWSKI
MCGILL UNIVERSITY
~
Springer-Verlag Wien GmbH
This volume contains 82 illustrations
This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks.
© 2001 by Springer-Verlag Wien Originally published by Springer-Verlag Wien New York in 2001
SPIN 10862933
In order to make this volume available as economically and as rapidly as possible the authors' typescripts have been reproduced in their original forms. This method unfortunately has its typographical limitations but it is hoped that they in no way distract the reader.
ISBN 978-3-211-83684-2 DOI 10.1007/978-3-7091-2780-3
ISBN 978-3-7091-2780-3 (eBook)
PREFACE Many solid materials - composites, granular media, metals, biomaterials, etc. - display microstructures of several length scales, oftentimes accompanied by a non-deterministic disorder. A better understanding and prediction of the resulting multiscale and random nature
(~f such
materials mesoscopic and/or
macroscopic properties requires a modeling approach based on a combination of probabilistic concepts with methods of mechanics. The present course was organized to provide an introduction to this subject through a self-contained series
~f
lectures by five mechanicians, materials
scientists and mathematicians working in (micro)mechanics of random media. First, motivated by a review of advanced experimental techniques for the microstructure description, and by typical results involving fluctuations present in plasticity, damage and fracture phenomena, basic tools of applied probability and random processes have been introduced. At the second stage, mechanics of random media was presented from the standpoint of approximate solutions of partial differential equations with random coefficients. For example, static elasticity problems in random media were studied by means of perturbation expansion of the random stress and strain .fields, while bounds on elastic moduli were derived from variational principles. This approach was illustrated by optimal microstructures.
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dynamic probl
