Biomedical Engineering Reference
In-Depth Information
(a)
(b)
(c)
FIGURE 4.1
Morphology of basic composite inclusions: (a) particle, (b) fiber, and (c) platelet.
vary in size and shape within a category. For example, particulate inclusions may be spherical, ellipsoi-
dal, polyhedral, or irregular. If one phase consists of voids, filled with air or liquid, then the material
is known as a cellular solid. If the cells are polygonal, then the material is a honeycomb; if the cells are
polyhedral, then it is a foam. It is necessary in the context of biomaterials to distinguish the above struc-
tural cells from biological cells, which occur only in living organisms. In each composite structure, we
may moreover make the distinction between random orientation and preferred orientation.
4.2 Bounds on Properties
Mechanical properties of many composite materials depend on structure in a complex way; however, for
some structures, the prediction of properties is relatively simple. The simplest composite structures are
the idealized Voigt and Reuss models, shown in Figure 4.2. The dark and light areas in these diagrams
represent the two constituent materials in the composite. In contrast to most composite structures, it is
easy to calculate the stiffness of materials with the Voigt and Reuss structures, since in the Voigt struc-
ture the strain is the same in both constituents; in the Reuss structure, the stress is the same. The Young
modulus,
E
, of the Voigt composite is
EEVE
=
+
[
1
−
V
]
(4 .1)
ii
m
i
where
E
i
is the Young modulus of the inclusions,
V
i
is the volume fraction of inclusions, and
E
m
is
the Young modulus of the matrix. The Voigt relation for the stiffness is referred to as the rule of
mixtures.
(a)
(b)
(c)
FIGURE 4.2
Voigt (a) laminar; (b) fibrous; and Reuss (c) composite models, subjected to tension force indicated
by arrows.
