INTRODUCTION
TO
CONTINUUM MECHANICS
FOR
ENGINEERS
(REVISED EDITION)
2004
By
Ray M. Bowen
Professor of Mechanical Engineering
President Emeritus
Texas A&M University
(First Edition Originally Published By Plenum Press 1989 as Volume 39)
(of Mathematical Concepts and Methods in Science and Engineering)
(ISBN 0306430509)
(Series Editor: Angelo Miele)
Copyright Ray M. Bowen
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Preface (First Edition)
This textbook is intended to introduce engineering graduate students to the essentials of
modern Continuum Mechanics.
The objective of an introductory course is to establish certain
classical continuum models within a modern framework.
Engineering students need a firm
understanding of classical models such as the linear viscous fluids (NavierStokes theory) and
infinitesimal elasticity.
This understanding should include an appreciation for the status of the
classical theories as special cases of general nonlinear continuum models.
The relationship of the
classical theories to nonlinear models is essential in light of the increasing reliance, by engineering
designers and researchers, on prepackaged computer codes.
These codes are based upon models
which have a specific and limited range of validity.
Given the danger associated with the use of
these computer codes in circumstances where the model is not valid, engineers have a need for an
in depth understanding of continuum mechanics and the continuum models which can be
formulated by use of continuum mechanics techniques.
Classical continuum models and others involve a utilization of the balance equations of
continuum mechanics, the second law of thermodynamics, the principles of material frame
indifference and material symmetry.
In addition, they involve linearizations of various types.
In
this text, an effort is made to explain carefully how the governing principles, linearizations and
other approximations combine to yield classical continuum models.
A fundamental understanding
of these models evolve is most helpful when one attempts to study models which account for a
wider array of physical phenomena.
This book is organized in five chapters and two appendices.
The first appendix contains
virtually all of the mathematical background necessary to understand the text.
The second
appendix contains specialized results concerning representation theorems.
Because many new
engineering graduate students experience difficulties with the mathematical level of a modern
continuum mechanics course, this text begins with a one dimensional overview.
Classroom
experience with this material has shown that such an overview is helpful to many students.
Of
course, more advanced students can proceed directly to the Chapter II.
Chapter II is concerned
with the kinematics of motion of a general continuum.
Chapter III contains a discussion of the
governing equations of balance and the entropy inequality for a continuum.
The main portion of
the text is contained in Chapter IV.
This long chapter contains the complete formulation of various
general continuum models.
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