Continuum mechanics deals with the change of shape (deformation) of bodies subjected to external mechanical and thermal loads. However, before we can discuss the physical laws governing deformation, we must develop measures that characterize and quantify it. This is the subject described by the kinematics of deformation. Kinematics does not deal with predicting the deformation resulting from a given loading, but rather with the machinery for describing all possible deformations a body can undergo.

The continuum particle

A material body B bounded by a surface ∂B is represented by a continuous distribution of an infinite number of continuum particles. On the macroscopic scale, each particle is a point of zero extent much like a point in a geometrical space. It should therefore not be thought of as a small piece of material. At the same time, it has to be realized that a continuum particle derives its properties from a finite-size region ℓ on the micro scale (see Fig. 3.1). One can think of the properties of the particle as an average over the atomic behavior within this domain. As one moves from one particle to its neighbor the microscopic domain moves over, largely overlapping the previous domain. In this way the smooth field-like behavior we expect in a continuum is obtained. A fundamental assumption of continuum mechanics is that it is possible to define a length ℓ that is large relative to atomic length scales and at the same time much smaller than the length scale associated with variations in the continuum fields.