Biomedical Engineering Reference
In-Depth Information
5.3 High- and low-fidelity models for CFCC nanocomposites.
combinations of individual composite material phases to achieve desired
material performance. The model management framework [3, 4], besides
managing the models and scales, is also well suited to control hierarchical
parallelism. The natural hierarchy is molecular dynamics (MD) within the
cohesive finite element method (CFEM) within design under uncertainty,
using a mixed programming model SHMEM
TM
by SGI for CFEM and
MPI for MD and the uncertainty modeling. Both MD and the uncertainty
quantification (via quasi-Monte Carlo integration) can use 1000 processors,
and CFEM 10, so 1000 uncertainty quantification groups of 10 CFEM
groups of 1000 HMC processors is 10
7
processors, nearing exascale.
Material design analyses of the model system have been performed to
understand the morphology-related parameters that must be controlled for
optimal targeted set of properties. The application of the design tool is
focusing on the continuous fiber ceramic composite (CFCCs) models of
SiC-Si
3
N
4
nanocomposites (Fig. 5.3). The second phase (circles and
cylinders) are the SiC fibers that have higher elastic modulus and higher
creep resistance (E) but lower yield stress and fracture toughness, than that
of the primary Si
3
N
4
phase. The problem is to design the most suitable
CFCC, with maximum strength and creep resistance for a set of external
temperatures T, where the number of design variables will depend on
whether the simulation tests are run on the 2D or 3D model. The design
variables to be considered in the nanocomposite design optimization
problem, for the 2D model, are the fiber diameter (d) and the external
temperature (T). For the 3D model, the design variables to be considered are
the fiber diameter (d), the length of fibers (l) and the external temperature
(T). The problem definition in standard form is:
minimize: f
ð
d
;
l
;
T
Þ¼fs
U
ð
d
;
l
;
T
Þ; e
c
ð
d
;
l
;
T
Þg
½
5
:
1
l
min
l
l
max
and T
¼
1500
C
subject to: d
min
d
d
max
