338
12 Carbon-Nanotube Reinforced Polymers
been damaged, rather than the composite structure. This is a continuing reliability
problem with SHM.
Dai et al. [32] use a different approach, in that a separate CNT-array sensor
is embedded within the composite structure, and an inverse problem is used to
determine the state of the structure. In this sense, their approach is similar to ours
in philosophy, except that we are not embedding our sensors. Furthermore, [32] use
electrical impedances as the measured data for inversion, which is what we do, but
their approach is based on electrical impedance tomography (EIT) to acquire and
invert the data. The sensor array used in EIT is conductive and not inductive, as
in eddy-current inversion. By conductive, we mean that the sensor is in electrical
contact with the structure. The resulting electromagnetic model produces a rather
ill-posed inverse problem that is sensitive to modeling errors and measurement
noise. For that reason, [32] uses a simplified linear process that uses the maximum
a posteriori (MAP) algorithm to solve the inverse problem. Furthermore, this
approach does not appear to be amenable to more complex (and realistic) problems
that include anisotropies and random distributions of anomalies.
12.8.7 Inverse Problem No. 2: Characterizing the CNT via
ESR
We can use electron-spin resonance (ESR) as a method of characterizing the CNT,
in much the same way that nuclear magnetic resonance (NMR) maps biological
structures. That would be a straightforward application of the spintronics theory
that we just developed. The method would work at GHz frequencies, rather than
MHz, as in MRI, but we expect to work at GHz and higher for NDE of CNT in any
case. This would be an interesting application of our spiral coil models in VIC-3D®.
Information from the absorption curve of Fig. 12.9 could be used for this. It seems
likely that if the environment of the spins changes, perhaps because of stresses, then
the crystal-field would also change, causing the spin-Hamiltonian to change with it.
This would cause the eigenvalues to change to some degree that would have to be
determined numerically, thereby shifting the center of the absorption curve.
12.8.8 What Does VIC-3D® Need?
Refer to Fig. 12.17. The anomalous region, which will be the CNT structure,
is embedded in a host, which at this time is isotropic and could be air. VIC3D® expects to be given the usual electromagnetic parameters, namely complex
conductivity and magnetic permeability, that are to be assigned to each voxel in
the anomalous region. The parameters can be (bi)anisotropic and stochastic and
even frequency dependent. The results of the quantum-mechanical models are
12 Carbon-Nanotube Reinforced Polymers
been damaged, rather than the composite structure. This is a continuing reliability
problem with SHM.
Dai et al. [32] use a different approach, in that a separate CNT-array sensor
is embedded within the composite structure, and an inverse problem is used to
determine the state of the structure. In this sense, their approach is similar to ours
in philosophy, except that we are not embedding our sensors. Furthermore, [32] use
electrical impedances as the measured data for inversion, which is what we do, but
their approach is based on electrical impedance tomography (EIT) to acquire and
invert the data. The sensor array used in EIT is conductive and not inductive, as
in eddy-current inversion. By conductive, we mean that the sensor is in electrical
contact with the structure. The resulting electromagnetic model produces a rather
ill-posed inverse problem that is sensitive to modeling errors and measurement
noise. For that reason, [32] uses a simplified linear process that uses the maximum
a posteriori (MAP) algorithm to solve the inverse problem. Furthermore, this
approach does not appear to be amenable to more complex (and realistic) problems
that include anisotropies and random distributions of anomalies.
12.8.7 Inverse Problem No. 2: Characterizing the CNT via
ESR
We can use electron-spin resonance (ESR) as a method of characterizing the CNT,
in much the same way that nuclear magnetic resonance (NMR) maps biological
structures. That would be a straightforward application of the spintronics theory
that we just developed. The method would work at GHz frequencies, rather than
MHz, as in MRI, but we expect to work at GHz and higher for NDE of CNT in any
case. This would be an interesting application of our spiral coil models in VIC-3D®.
Information from the absorption curve of Fig. 12.9 could be used for this. It seems
likely that if the environment of the spins changes, perhaps because of stresses, then
the crystal-field would also change, causing the spin-Hamiltonian to change with it.
This would cause the eigenvalues to change to some degree that would have to be
determined numerically, thereby shifting the center of the absorption curve.
12.8.8 What Does VIC-3D® Need?
Refer to Fig. 12.17. The anomalous region, which will be the CNT structure,
is embedded in a host, which at this time is isotropic and could be air. VIC3D® expects to be given the usual electromagnetic parameters, namely complex
conductivity and magnetic permeability, that are to be assigned to each voxel in
the anomalous region. The parameters can be (bi)anisotropic and stochastic and
even frequency dependent. The results of the quantum-mechanical models are