Homogenization Techniques for Composite Media Lectures Delivered at
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272 Homogenization Techniques for Composite Media Lectures Delivered at the CISM International Center for Mechanical Sciences Udine, Italy, July 1-5, 1985
Edited by E. Sanchez-Palencia and A. Zaoui
Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo
Editors Enrique Sanchez-Palencia Universitd Paris VI 4, place Jussieu, F - 7 5 2 3 0 Paris
Andr~ Zaoui Universit6 Paris Xlll av. Jean Baptiste CIL=ment, F-93430 Villetaneuse
ISBN 3-540-17616-0 Springer-Verlag Berlin Heidelberg NewYork ISBN 0-387-17616-0 Springer-Verlag New York Berlin Heidelberg This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. Duplication of this publication or parts thereof is only permitted under the provisions of the German Copyright Law of September 9, 1965, in its version of June 24, 1985, and a copyright fee must always be paid. Violations fall under the prosecution act of the German Copyright Law. © Springer-Verlag Berlin Heidelberg 1987 Printed in Germany Printing: Druckhaus Beltz, Hemsbach/Bergstr.; Bookbinding: J. 'Sch&ffer GmbH & Co. KG., GrL~nstadt 2153/3140-543210
PREFACE
This book contains the written version of a course
delivered
in July
1985 at the International Centre for Mechanical Sciences, Udine, Italy.
One part of the course
(lectures by Caillerie,
and Suquet) dealt with periodic media
L~vy,
Sanchez-Palencia
(laminated solids,
various kinds
of porous media, etc.). Special attention was paid to the local stress field in composite materials,
generation of cracks and other forms of
damage. The two-scale procedure yields, beside the global properties,
a
good description of the local state of stress which is responsible for the local failure Of a composite. Suggestions were given for the numerical solution of the problems.
Another
part
of
the
course
(lectures
by
cerned with randomly inhomogeneous media crystals,
...).
Willis
and
Zaoui)
was con,
(disordered composites,
Variational methods for determining the bounds
polyof
the
overall moduli from practical statistical information were presented, as well as simplified methods for special cases and applications
(plastic
anisotropy correlated with texture development, plasticity of multiphase metals,
etc.).
The course gathered together scientists and research engineers specializing in the fields of suspensions and sedimentation,
composite media,
plates, polycrystals, plasticity, etc., and gave everyone an opportunity to exchange ideas and to discuss problems.
It is our pleasant duty to express our sincere thanks to the authorities and staff of CISM for the organization of the course.
Paris,
November E.S.P., A.Z.
1986
CONTENTS
PART NON ~
II
PLATE ~ R Y by m
I
AND CONDUCTION IN F D. C a i l l e r i e
Homogenization i n E l a s t i c i t y
~
~ I T E S
2
......................
I°
--
I
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