Mechanical Modeling of Material Behavior - Continuum Mechanics of Anisotropic Materials - page 5

Fig. 1.2 The three types of motion possible for an object
A translational motion is illustrated in Fig. 1.2a . In pure rotational motion the
velocities of all the points of the moving object, at any instant, are proportional to
the distance of the point from one single fixed axis. This situation is illustrated in
Fig. 1.2b in the special case where the fixed axis is perpendicular to the plane of the
page. A deformational motion (Fig. 1.2c ) is a motion in which some points on
the same object move relative to one another. It can be shown that the motion of any
object or material system can, at any time, be decomposed into the sum of
three motions, a translational motion, a rotational motion, and a deformational
motion. If there are many objects (e.g., molecules) and only average properties of
the ensemble are sought by statistical methods, the model is said to be one of
statistical mechanics.
These motions suggest three of the five types of models of objects used in
mechanics: the particle model, the rigid object model, and the deformable contin-
uum model. These models of objects are differentiated from one another on the
basis of the type of motion modeled. The particle model only emulates the transla-
tional motion of the object; the rigid object model emulates both translational and
rotational motion of the object; and the deformable continuum model emulates all
three types of motion. The first two models, the particle model and the rigid object
model, are described in mechanics topics dealing with statics and dynamics of
particles and rigid objects. The deformable continuum model is described in topics
dealing with the mechanics or strength of materials or in topics on elasticity and
fluid or continuum mechanics.
There is an important fourth category of model used in mechanics that overlaps
the first three model types; this category is the lumped parameter model, a very
important model type in mechanics. The particle model, rigid object model,
deformable continuum model, and the lumped parameter model are discussed in