To model the physical phenomena of deformation and fracture, described briefly in Chapter 1, a method based upon general principles which govern the variables representative of the state of the material medium is needed. The objective of this chapter is to present in a condensed form all the basic concepts that will be used in the following chapters. Two types of modelling are necessary: one, the so-called kinematical or mechanical modelling is concerned with the motions and forces in the continuum, and the second, the so-called phenomenological or physical modelling introduces the variables characterizing the phenomena under study.

The presentation given here is the result of the work of Germain as presented in a post graduate course and subsequently incorporated by one of the authors (Lemaitre) in his course, and also contained in Cours de mécanique des milieux continus cited in the bibliography of this chapter. This reference contains the details necessary for a deeper understanding of the concepts. Here, only the essential results are given, and the mathematical derivations have been largely omitted. The notation used is almost identical to that in the work referred to above which should help the reader who is anxious to go deeper into the subject.

The framework of mechanics presented here is based on the principle of virtual power. Although the basic idea was presented by D'Alembert as long ago as 1750, it is only, with the development of the variational methods of functional analysis in around 1970 (Duvaut, Lions, Nayroles), that systematic use of this principle has been made.