Theoretical models can never fully
represent the total
complexity of the
real world, but can only include certain
aspects that are important for
solving a certain
question or
problem. This is the whole idea behind creating
models. One only includes that which is
necessary and leaves out what is of no, or
neglectable,
influence (one hopes) on whatever is under
study. Often, most of the aspects that
are included are
approximated and/or
idealised.
Mechanical properties of a
material are defined by the
masses of, and
interactions between,
particles on a
molecular scale (one could go even smaller, with
quantum mechanics, or whatnot). However, the
scales of most
systems under review in
mechanical and
civil engineering (and many other everyday situations) are much bigger than that. For these systems one usually
dispenses with looking at the
molecular level and pretends that on a larger scale these materials are continuously spread out in the
physical space. This is what one calls a
continuum model.
A
property that is locally
attributed to the
continuum (for example, the
density) is in fact the result of the contributions of the
molecules in a small
space. The space should be
large enough to contain enough molecules for the
sum of their contributions to be
statistically stable; on the other hand, it should be
small enough in relation to the scale of the system under review to be able to speak of the properties defined at a single
point of said system.
This results in these properties being able to be interpreted as
functions of the
continuous physical space. These functions are sometimes called
fields, for example, the field of
temperature,
pressure (
scalar fields) or
velocity (a
vector field).
Support write-up for Fluid mechanics
Sources:
An adaptation of an excerpt from one of my college textbooks - node your homework
July 8, 2001