In this chapter we consider the deformation of a body due to the application of loads. We use the term "deformation" to signify the entire geometric change by which the points in a body in the initial state with all loads absent go to another configuration as a result of the action of loads. The aforementioned initial state we shall call the undeformed state, and the subsequent state occurring in the presence of loads we call the deformed state. The deformation, so defined, will be seen to include the following contributions for each element of a body:

1. Rigid-body translation and rotation 2. A dilatation contribution from changes in geometry associated with the vol-

ume change of the element 3. A distortion contribution from the remaining changes in geometry of the ele-

ment, which includes as an important contribution the change in angularity between line segments in the element

In later chapters we shall want to relate parts 2 and 3 of the deformation with the stresses in the body. In this regard you may remember from your physics courses that it was the relative movement between two atoms that gave rise to a variation in the bonding force between the atoms. Following a similar line of reasoning in this chapter, in anticipation of our desire 1<;) relate parts 2 and 3 above with stress, we shall be concerned with the relative movement between any two "adjacent" points (Le., points infinitesimally close to each other in the undeformed geometry). This study will also permit us to separate out and describe mathematically part 1 of the deformation.