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Multiscale Modeling and Simulation
of Composite Materials
and Structures
Young W. Kwon • David H. Allen
• Ramesh Talreja
Multiscale Modeling and
Simulation of Composite
Materials and Structures
Edited by:
Young W. Kwon
Naval Postgraduate School
Dept. of Mechanical and
Astronautical Engineering
Graduate School of Engineering
and Applied Sciences
Monterey, CA 93943
David H. Allen
University of Nebraska-Lincoln
College of Engineering
114 OTHM
Lincoln, NE 68588
Ramesh Talreja
Texas A&M University
Dept. Aerospace Engineering
Mail Stop 3141
College Station, TX 77843
Library of Congress Control Number: 2007930778
ISBN 978-0-387-36318-9
e-ISBN 978-0-387-68556-4
Printed on acid-free paper.
© 2008 Springer Science+Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York,
NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in
connection with any form of information storage and retrieval, electronic adaptation, computer
software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The
use in this publication of trade names, trademarks, service marks and similar terms, even if they are not
identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to
proprietary rights.
9 8 7 6 5 4 3 2 1
Ever since Democritus hypothesized the existence of the atom in the third
century BC , evidence of the existence of physical phenomena on extremely
small length scales has been accumulating. With the publication of
Copernicus’ book on the sun-centered solar system in 1543, evidence
began to pile up that physical phenomena also occur on extremely large
length scales. Today, it is not possible for us to put reliable bounds on
either extreme. Indeed, just as the span of time is potentially infinite, the
span of length may be unbounded.
Over the twentieth century, the most fundamental of sciences expanded
the span of length by many orders of magnitude. Now, in the twenty-first
century, one of the primary goals of science and technology seems to be
the quest to develop reliable methods for linking physical phenomena that
occur over multiple length scales. We now know that many vastly different
fields of science such as biology, cosmology, paleontology, atmospheric
physics, materials science, and even social sciences are faced with issues
involving multiple length scales.
Until recently, our computational tools did not seem to be sufficiently
powerful to engage in research activities focused on multiple length scales.
However, with the rise of the high-speed digital computer, we now have
the power to attempt to resolve scientific issues that were heretofore
beyond our reach. Consider a single example – the growth of a crack in
a ductile multigrain crystalline metal. Is this a problem in continuum
mechanics, or is it molecular in scale? Or is it even smaller, perhaps even
at the quantum scale? Evidence today seems to suggest that it is all of
these, and that the physical phenomena observed at any of these length
scales are indeed causatively linked to those on the neighboring length
scales. Therefore, it would seem that the scientific profession is faced with
a formidable challenge if predictive methodologies for such complicated
phenomena are to be forthcoming. In the words of one of our colleagues,
“A scientist loves a good challenge!”
vi Preface
In this text, we present recent work of 13 leaders in the field of multi-
scale mechanics, along with their coauthors, aimed at composite materials
and structures. It is our hope that you the reader will in turn be challenged
by these chapters, and that you will find your own paths to future develop-
ments in what amounts to one of the great problems of our time.
came out at the meeting “Advances in Multiscale Modeling of Composite
Material Systems and Components” held in Monterey, California organized
by him; Caitlin Wormesley, Greg Franklin, Carol Day, and Alex Greene of
Springer for their support; and Patricia Worster at University of Nebrska
for her dedicated service in editing all manuscripts.
Y.. Kwon
D.H. Allen
R. Talreja
The editors thank Peter Beaumont because the inception of this book
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