Chemistry Reference
In-Depth Information
the external forces acting on the medium and the resulting internal stress
and strain. Computational approaches range from simple closed-form ana-
lytical expressions to micromechanics and complex structural mechanics
calculations based on beam and shell theory. In this section, we introduce
some continuum methods that have been used in polymer nanocomposites,
including micromechanics models (e.g., Halpin-Tsai model, Mori-Tanaka
model and finite element analysis.) and the semicontinuum methods like
equivalent-continuum model and will be discussed in the next part.
9.2.2.1 MICROMECHANICS
Micromechanics are a study of mechanical properties of unidirectional
composites in terms of those of constituent materials. In particular, the
properties to be discussed are elastic modulus, hydrothermal expansion
coefficients and strengths. In discussing composites properties it is impor-
tant to define a
volume element
which is small enough to show the micro-
scopic structural details, yet large enough to present the overall behavior
of the composite. Such a volume element is called the
Representative Vol-
ume Element (RVE)
. A simple representative volume element can consists
of a fiber embedded in a matrix block, as shown in Fig. 9.3.
FIGURE 9.3
A Representative Volume Element (RVE). The total volume and mass of
each constituent are denoted by V and M, respectively. The subscripts m and f stand for
matrix and fiber, respectively.
