Functionally Graded Materials in Engineering - Structural Interfaces and Attachments in Biology - page 31

considered in [ 82 ] where it was indicated that the crack propagation can be retarded
by an appropriate grading of the material.
A stochastic multiscale approach to the fracture problem in FGMwas considered
in [ 83 ]. The probabilistic crack-driving forces and reliability were assessed
employing two stochastic methods, i.e., the dimensional decomposition method
and the Monte-Carlo simulation.
The effect of in-plane material grading on the stress concentration factor in an
FGM plate with a circular hole was numerically investigated in [ 84 ]. It was
demonstrated that the stress concentration can be reduced by varying the modulus,
gradually increasing it with the distance from the hole.
Contact problems of FGM have also received the close attention of researchers.
For example, Lee et al. investigated the effect of modulus of elasticity grading on
the indentation produced in an elastic half-space by a rigid indenter [ 85 ]. The
contact problem for an FGM layer subject to frictional sliding load applied by a
flat punch was investigated in [ 86 ].

2.4.7 Manufacturability

One of the most challenging aspects of engineering FGM is related to the difficulty
of manufacturing components with prescribed grading. These complications arise
from a very small dimensional scale of property variations. This problem, discussed
in a previous review [ 3 ] and other references, is particularly severe in case of
grading in the thickness direction. If grading occurs with respect to in-surface
coordinates, a larger scale usually permits a much easier reproduction of prescribed
gradients. Some of the recent studies relevant to the manufacture of FGM

components have been discussed in [ 10 , 87 , 88 ].

2.4.8 Biomedical Applications of FGM

Biomedical applications of FGM have not been extensively reviewed in the litera-
ture (e.g., [ 3 ]). Accordingly, we concentrate here on biomedical problems where
these materials either may be applied or have been considered.
Erisken et al. investigated viscoelastic and compressive properties of a bovine
osteochondral tissue and engineered constructs aiming at a better understanding of
grading in properties along the thickness enabling a smooth transition of loads [ 89 ].
A bi-phasic model of functionally graded soft tissues was analyzed to describe a
response to mechanical loading, accounting for geometric nonlinearities, rate-
dependence, and anisotropy in [ 90 ]. Willert-Porada reviewed possible applications
of biomimetic methods in design and fabrication of both a functionally graded
hard tissue implant and, surprisingly, applications such as diesel engine filters [ 10 ].