Figure 1: Diamond tool
cutter.
Consider a simple but typical
example that is depicted in Figure 1(a) The solid object
is partitioned into a diamond cutter (chip) and a shank
that is manufactured from functionally graded composition
of SiC and diamond. To control the composition, the
shank is subdivided into three parts: block region with
100% SiC, prismatic region with 80% SiC and 20% diamond,
and the transition region between them where the composition
is a gradual blend of the two materials. Ideally, the
blend should be smooth and may satisfy additional constraints
prescribed by the designer or constrained by the manufacturing
process. Figure 1(b) shows an interpolation between
the respective fractions of the two materials that vary
linearly with the distance between the two regions and
add up to 1 at every point of the solid.
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(d) |
Figure 2: Graded refractive
index (GRIN) within the Y-shaped solid.
The example in Figure 2 shows a parabolic
distribution of the graded refractive index (GRIN) within
the Y-shaped solid. Many applications of GRIN are found
in optical fibers for communication and precision lens
for micro-optics. The material feature ( geometry,
where material properties are known ) is the Y-shaped
one-dimensional skeleton constructed as the union of the
three axes of the cylinders. Figure 2(b) shows a
magnified planar section of the distribution.
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