98
4 Application of the Set-Theoretic Algorithm to CFRP’s
0
90
0
0mm
0.1mm
0.2mm
0.3mm
0.4mm
152.4mm x 152.4mm
x y
σ = σ = σ = 100
z
Fig. 4.9 Model for studying the laminated engineering composite structure shown in Fig. 4.8
without the voids
Microcrack
W
0mm
0.1mm
0.2mm
0.3mm
0
90
0
0.5mm x 0.5mm
Fig. 4.10 Model for studying the laminated engineering composite structure shown in Fig. 4.8
with a single void microcrack. The width of the void is W , and the depth into the figure is 0.5 mm.
This structure is embedded in an isotropic graphite-epoxy host whose conductivity is 20,000 S/m,
and is 0.3 mm high
the structure is excited by the T probe shown in Fig. 4.7 as it is scanned past the
microcrack from −1.6 mm to +1.6 mm at a frequency of 1 GHz.
To that end, we apply model-based inversion, starting with the blending functions
that define the surrogate interpolation table. These are shown in Fig. 4.11 for the
nodal values W = (0.00, 0.025, 0.050) mm. The VIC-3D®-grid used to generate
these functions was N x = 256, N y = 8, N z = 16, which was sufficient to capture
the variations in W . The test value of W was 0.030 mm.
The result of the inversion is shown in Table 4.3. Not only is the solution
virtually identical to the test value, but all 500 initial starting points in NLSE
converged to the same global minimum. The excellent quality of the inversion
testifies to the fact that the blending functions of Fig. 4.11 are highly sensitive
to W .
4 Application of the Set-Theoretic Algorithm to CFRP’s
0
90
0
0mm
0.1mm
0.2mm
0.3mm
0.4mm
152.4mm x 152.4mm
x y
σ = σ = σ = 100
z
Fig. 4.9 Model for studying the laminated engineering composite structure shown in Fig. 4.8
without the voids
Microcrack
W
0mm
0.1mm
0.2mm
0.3mm
0
90
0
0.5mm x 0.5mm
Fig. 4.10 Model for studying the laminated engineering composite structure shown in Fig. 4.8
with a single void microcrack. The width of the void is W , and the depth into the figure is 0.5 mm.
This structure is embedded in an isotropic graphite-epoxy host whose conductivity is 20,000 S/m,
and is 0.3 mm high
the structure is excited by the T probe shown in Fig. 4.7 as it is scanned past the
microcrack from −1.6 mm to +1.6 mm at a frequency of 1 GHz.
To that end, we apply model-based inversion, starting with the blending functions
that define the surrogate interpolation table. These are shown in Fig. 4.11 for the
nodal values W = (0.00, 0.025, 0.050) mm. The VIC-3D®-grid used to generate
these functions was N x = 256, N y = 8, N z = 16, which was sufficient to capture
the variations in W . The test value of W was 0.030 mm.
The result of the inversion is shown in Table 4.3. Not only is the solution
virtually identical to the test value, but all 500 initial starting points in NLSE
converged to the same global minimum. The excellent quality of the inversion
testifies to the fact that the blending functions of Fig. 4.11 are highly sensitive
to W .