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Electrical impedance tomography (EIT) is a non-invasive method of spatially mapping the electrical conductivity distribution of a domain based on a limited number of externally collected voltage-current measurements. This modality has been widely explored in the state of the art for damage detection, shaping, and localization in conductive composites (e.g. continuous carbon fiber composites and various nanofiller-modified continuous glass fiber composites) for purposes such as nondestructive evaluation (NDE), structural health monitoring (SHM), and embedded sensing. Mathematically, EIT is an ill-posed inverse problem that requires regularization to solve. To date, materials-focused practitioners of EIT have used relatively simple forms of regularization including, among others, Tikhonov regularization and the discrete Laplace operator (i.e. a smoothness prior). This is limiting because much more advanced types of regularization exist and have potential to significantly improve EIT for material state awareness. Therefore, in this work we propose and experimentally validate a novel mixedform regularization for the EIT inverse problem. In this approach, the discrete Laplace operator or smoothness prior is combined with a conditionally Gaussian prior (i.e. a focal prior). This mixed formulation has the benefit of simultaneously filtering out oscillatory background conductivity perturbations (via the smoothness prior) while still permitting outliers in the solution space (via the focal prior), which is expected to be the case for highly localized damage features in a background of otherwise zero change. The proposed mixed formulation was experimentally validated on two different three-dimensional composites: a carbon black (CB)-modified glass fiber/epoxy tube and a carbon fiber/epoxy laminate shaped as a representative NACA airfoil. Both composite specimens were subject to low-velocity impact damage via a drop-tower rig. It was found that the mixed smoothness + conditionally Gaussian regularization approach markedly outperforms the traditional smoothnessonly regularization, which allows for much clearer visualization of the damaged state of the material. This work demonstrates the importance of researching advanced regularization methods for materials imaging via EIT.

Carbon fiber reinforced polymers (CFRPs) are valued in aerospace and other weight-conscious applications for their high strength-to-weight ratio. However, with the adoption of these lightweight materials emerges challenges not seen in traditional monolithic materials such as complex internal (i.e. outwardly invisible) damages like delamination or fiber failure in the structure. Robust methods of damage detection and health monitoring are therefore important. It is also desirable to utilize an intrinsic property of these materials, such as electrical conductivity, as an indicator of damage to render the material as self-sensing. Electrical impedance tomography (EIT) has been widely explored for damage detection and health monitoring in self-sensing materials. To date, however, studies involving EIT have been largely limited to materials with less electrical anisotropy than is seen in CFRPs and using only edge-placed electrodes (e.g. electrodes placed on the edges of a plate). These limitations are important because the inability to handle highly electrically anisotropic materials precludes EIT from a great number of existent CFRP structures. Furthermore, many real structures lack well-defined edges on which electrodes can be placed. In this paper, we tackle these challenges by presenting a preliminary study into the role of EIT sensitivity matrix formulation and surface-mounted electrodes on damage detection and localization in CFRPs. In our approach, the conductivity is modeled as being anisotropic, and the sensitivity matrix is formed using three methods — with respect to a scalar multiple of the conductivity tensor, the out-of-plane conductivity, and the in-plane conductivity. It was found that through-hole damage can be adeptly identified using the combination of surface-mounted electrodes and a sensitivity matrix formed with respect to either a scalar multiple of the conductivity tensor or the in-plane conductivity. The findings presented in this work take an important step towards translating EIT out of the laboratory and into real applications on CFRPs.

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