Elasticity, Fracture and Flow with Engineering and Geological Applic
IN this monograph I have attempted to set out, in as elemen tary a form as possible, the basic mathematics of the theories of elasticity, plasticity, viscosity, and rheology, together with a discussion of the properties of the materials involved and the
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Elasticity, Fracture and Flow with Engineering and Geo1vgical A . . plications
J. C. JAEGER Professor of Geophysics in the Australian National UnifJernty
LONDON
CHAPMAN & HALL
First published 1956
by Methuen & Co Ltd
Second edition 19611 RePrinted with corrections 1964 Third edition 1969 First published as a Science Paperback 1971 by Chapman and Hall Ltd 11 New Fetter Lane. London EC4P 4EE Reprinted 1974. 1978
f. W. Arrowsmith Ltd. Bristol ISBN 0 412208903
© f.
C. Jaeger. 1969
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photo-copying, recording, or otherwise, without the prior written permission of the publisher.
This paperback edition is sold subject to the condition that it shall not, by way of trade or otherwise, be lent, resold, hired out, or otherwise circulated without the publisher's prior consent in any form of binding or cooer other than that in which it is published and without a similar condition including this condition being imposed on the subsl'lJIfll1ltpurchDser.
ISBN-13: 978-0-412-20890-4 e-ISBN-13: 978-94-011-6024-7 DOl: 10.1007/978-94-011-6024-7
Distributed in the U.S.A. by Halsted Press, a division of John Wiley & Sons, Inc. New York
PREFACE IN this monograph I have attempted to set out, in as elementary a form as possible, the basic mathematics of the theories of elasticity, plasticity, viscosity, and rheology, together with a discussion of the properties of the materials involved and the way in which they are idealized to form a basis for the mathematical theory. There are many mathematical text-books on these subjects, but they are largely devoted to methods for the solution of special problems, and, while the present book may be regarded as an introduction to these, it is also intended for the large class of readers such as engineers and geologists who are more interested in the detailed analysis of stress and strain, the properties of some of the materials they use, criteria for flow and fracture, and so on, and whose interest in the theory is rather in the assumptions involved in it and the way in which they affect the solutions than in the study of special problems. The first chapter develops the analysis of stress and strain rather fully, giving, in particular, an account of Mohr's representations of stress and of finite homogeneous strain in three dimensions. In the second chapter, on the behaviour of materials, the stress-strain relations for elasticity (both for isotropic and simple anisotropic substances), viscosity, plasticity and some of the simpler rheological models are described. Criteria for fracture and yield, including Mohr's, Tresca's and von Mises's, are discussed in detail with some applications. In the third chapter the equations of motion and equilibrium are derived, and a number of special problems are solved. These have been chosen partly because of their practical importance and partly to illustrate the differences in behaviour betwe
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