Mechanical Modeling of Material Behavior - Continuum Mechanics of Anisotropic Materials - page 6

the next four sections. The fifth categories of mechanics models, statistical models,
are not discussed in this volume.
After this chapter, the remainder of the topic is an elaboration of the deformable
continuum model.

1.5 The Particle Model

The particle model is the simplest model in the hierarchy of models in classical
mechanics. This model of an object considers the entire mass of the object as
located at the mass center and only the translational motion of the mass center is
modeled. Thus the image of the model shown in Euclidean space in Fig. 1.1 shrinks
to a mass point located at the mass center, as illustrated in Fig. 1.3 . Since the mass
center is a point, the particle model is a point model; rotational motions and
deformations of the object are neglected. The English natural philosopher Isaac
Newton (1642-1727) created the particle model when he took the sun and a planet
to be particles and used his universal law of gravitation and his second law to
provide an analytical derivation of the three empirical laws of the German
astrologer-astronomer Johannes Kepler (1571-1630). In particular, Newton's
model showed that the planets moved around the sun in elliptical orbits, a fact
previously established by Kepler's observational data. Moments and rotational
motions are not considered in the particle model; they are considered in the rigid
object model.
The modeling structure described above may be employed as a framework for
the statement of Newton's second law. This may be accomplished by letting
the vector p denote the position of a typical point in the mathematical model of

The Mathematical Model
of the Object. The Real Object

mass center

A Cartesian Reference
Coordinate System

THE REAL WORLD EUCLIDIAN 3 SPACE

Fig. 1.3 The particle model of a real object