文档介绍：T. Belytschko, Continuum Mechanics, December 16, 1998 1
CHAPTER 3
CONTINUUM MECHANICS
by Ted Belytschko
Northwestern University
Copyright 1996
DRAFT
INTRODUCTION
Continuum mechanics is an essential building block of nonlinear finite
element analysis, and a mastery of continuum mechanics is essential for a good
understanding of nonlinear finite elements. This chapter summarizes the
fundamentals of nonlinear continuum mechanics which are needed for a
development of nonlinear finite element methods. It is, however, insufficient for
thoroughly learning continuum mechanics. Instead, it provides a review of the
topics that are particularly relevant to nonlinear finite element analysis. The
content of this chapter is limited to topics that are needed for the remainder of the
book.
Readers who have little or no familiarity with continuum mechanics
should consult texts such as Hodge (1970), Mase and Mase (1992), Fung (1994),
Malvern (1969), or Chandrasekharaiah and Debnath (1994). The first three are
the most elementary. Hodge (1970) is particularly useful for learning indicial
notation and the fundamental topics. Mase and Mase (1992) gives a concise
introduction with notation almost identical to that used here. Fung (1994) is an
interesting book with many discussions of how continuum mechanics is applied.
The text by Malvern (1969) has e a classic in this field for it provides a
very lucid prehensive description of the field. Chandrasekharaiah and
Debnath (1994) gives a thorough introduction with an emphasis on tensor
notation. The only topic treated here which is not presented in greater depth in all
of these texts is the topic of objective stress rates, which is only covered in
Malvern. Monographs of a more advanced character are Marsden and Hughes
(1983), Ogden (1984) and Gurtin (). Prager (1961), while an older book, still
provides a useful description of continuum mechanics for the reader with an
intermediate background. The classi