Biomedical Engineering Reference
In-Depth Information
Chapter 1
Mechanical Modeling of Material Behavior
1.1
Introduction
The typical types of models that have been employed in the analysis of the
mechanical behavior of material objects are described in this chapter. Specifically,
descriptions of the various model types employed in mechanics, namely the particle
model, the rigid object model, the deformable continuum model, and the lumped
parameter model are described. The modeler should view these model types as tools
and the task of the modeler is to select the proper tool for the problem at hand.
The content of this chapter is not material that can be learned by rote memoriza-
tion. It is material that must be thought about and practiced in order to acquire a
modeler's skill. In the next section conservation principles, control volumes, and
free object diagrams are discussed. In the section that follows, the first problem in
modeling, the concept of time, is considered, then that of space. In the next section,
the relationship between models and the real physical world is discussed. Four
sections that describe particle models, rigid object models, continuum models, and
lumped parameter models, respectively, follow a section on the types of models
used in mechanics. The final section concerns two philosophical questions related
to mechanical modeling, reductionism, and determinism.
1.2 Conservation Principles, Control Volumes,
and Free Object Diagrams
There is an aspect of the application of conservation principles of mechanics (those
of mass, momentum, angular momentum, energy, etc.) that is an artisan-like skill
that requires some experience on the part of the modeler. Most engineering students
acquire this skill when they learn to construct “free object diagrams” to apply
Newton's laws to solid objects in a course on statics or to draw “control volumes”
to apply the conservation principles of mechanics to fluids. These diagrams or
