Deformation and configuration

The present chapter is devoted to the study of geometric changes in a continuous medium that is in static or dynamic equilibrium under the action of some stimuli, such as mechanical, thermal, or other types of forces. The change of geometry or rate of change of geometry of a continuous medium can be used as a measure of so-called strains or strain rates, which are responsible for inducing stresses in the continuum. In the subsequent chapters, we will study stresses and physical principles that govern the mechanical response of a continuous medium. The study of geometric (or rate of geometric) changes in a continuum without regard to the stimuli (forces) causing the changes is known as kinematics.

Consider a continuous body of known geometry, material constitution, and loading in a three-dimensional space; the body may be viewed as a set of particles, each particle representing a large collection of molecules, having a continuous distribution of matter in space and time. Examples of such a body are provided by a diving board, the artery in a human body, a can of soda, and so on. Suppose that the body is subjected to a set of forces that tend to change the shape of the body.