Page 14 - Introduction to Continuum Mechanics

Preface to the First Edition
This text is prepared for the purpose of introducing the concept of continuum mechanics
to beginners in the field. Special attention and care have been given to the presentation of the
subject matter so that it is within the grasp of those readers who have had a good background
in calculus, some differential equations, and some rigid body mechanics. For pedagogical
reasons the coverage of the subject matter is far from being extensive, only enough to provide
for a better understanding of later courses in the various branches of continuum mechanics
and related fields. The major portion of the material has been successfully class-tested at
Rensselaer Polytechnic Institute for undergraduate students. However, the authors believe
the text may also be suitable for a beginning graduate course in continuum mechanics.
We take the liberty to say a few words about the second chapter. This chapter introduces
second-order tensors as linear transformations of vectors in a three dimensional space. From
our teaching experience, the concept of linear transformation is the most effective way of
introducing the subject. It is a self-contained chapter so that prior knowledge of linear
transformations, though helpful, is not required of the students. The third-and higher-order
tensors are introduced through the generalization of the transformation laws for the second-
order tensor. Indicial notation is employed whenever it economizes the writing of equations.
Matrices are also used in order to facilitate computations. An appendix on matrices is included
at the end of the text for those who are not familiar with matrices.
Also, let us say a few words about the presentation of the basic principles of continuum
physics. Both the differential and integral formulation of the principles are presented, the
differential formulations are given in Chapters 3,4, and 6, at places where quantities needed
in the formulation are defined while the integral formulations are given later in Chapter 7.
This is done for a pedagogical reason: the integral formulations as presented required slightly
more mathematical sophistication on the part of a beginner and may be either postponed or
omitted without affecting the main part of the text.
This text would never have been completed without the constant encouragement and advice
from Professor F. F. Ling, Chairman of Mechanics Division at RPI, to whom the authors wish
to express their heartfelt thanks. Gratefully acknowledged is the financial support of the Ford
Foundation under a grant which is directed by Dr. S. W. Yerazunis, Associate Dean of
Engineering. The authors also wish to thank Drs. V. C. Mow and W. B. Browner, Jr. for their
many useful suggestions. Special thanks are given to Dr. H. A. Scarton for painstakingly
compiling a list of errata and suggestions on the preliminary edition. Finally, they are indebted
to Mrs. Geri Frank who typed the entire manuscript.

W. Michael Lai
David Rubin
Erhard Krempl
Division of Mechanics, Rensselaer Polytechnic Institute
September, 1973

XIII