Biomedical Engineering Reference
In-Depth Information
0.5
Experiment
FE
0.4
0.3
0.2
0.1
0.0
500 µm
0.00
0.01
0.02
0.03
0.04
ε
trans
0.025
0.000
-0.025
-0.050
Macro Exp
Matrix Exp
Fiber Exp
Macro FE
Matrix FE
Fiber FE
-0.075
-0.100
-0.125
0.00
0.01
0.02
0.03
0.04
ε
long
Fig. 14 Multiscale validation of a micromechanical model. (Upper left) A dual channel 4X
confocal image of a surrogate construct shows the red fluorescent beads in the gel matrix and the
green fluorescent beads in the fiber that were used for microscopic and macroscopic strain
measurements. (Upper right) Micromechanical FE model stress-strain predictions were in excellent
agreement with the experimental data. (Middle left) The constrained surrogate model displayed
considerable heterogeneity in transverse strain. (Middle right) Microscopic and macroscopic strain
measurement results show that the macroscopic transverse strain (black line) was not representative
of the microscopic fiber strain (green line) or matrix strain (red line). The error bars represent the
standard deviation computed for all samples. (Bottom) Micromechanical FE model of the surrogate.
Green elements represent the fibers and red elements represent the gel matrix
matched by the experimentally measured values (NRMSE = 0.018), while pre-
dictions for the microscopic transverse matrix strain were reasonable but not as
accurate (NRMSE = 0.190). When simulations were performed using coefficients
that varied by a single standard deviation, all of the predictions were closely
bounded by this uncertainty. A sensitivity study was then performed in which the
inter-fiber spacing and the inter-fiber matrix material properties were varied.
The results of this work indicate that the micromechanical model was able to
accurately predict the strains at both the macroscopic and microscopic level,
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