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.

The numerous approaches used in micromechanics can be classified into four broad categories: perturbation methods, self-consistent methods of truncation of a hierarchy, variational methods, and the model methods. In detail we will consider the self-consistent methods applied to linear elastic problems, based on some approximate and closing assumptions for truncating of an infinite system of integral equations involved and their approximate solution. We consider multiparticle effective field methods, effective medium methods, the Mori-Tanaka method, differential methods and some others. This review article tends to concentrate on methods and concepts, their possible generalizations, and connections of different methods, rather than explicit results. In the framework of a unique scheme, we undertake an attempt to analyze the wide class of statical and dynamical, local and nonlocal, linear and nonlinear micromechanical problems of composite materials with deterministic (periodic and non-periodic) and random (statistically homogeneous and inhomogeneous, so-called graded) structures, containing coated or uncoated inclusions of any shape and orientation and subjected to coupled or uncoupled, homogeneous or inhomogeneous, external fields of different physical natures. The last section contains a discussion of prospects for future work. The article includes 540 references.

No abstract

No abstract

No abstract