On micro to mesoscale homogenization of electrical properties for damaged laminated composites (and their potential applications in electrical tomography)

Abstract

Efficient and optimal use of composites in structures requires tools to monitor and capture the complex degradation that can occur within the laminates over time. Structural health monitoring (SHM) techniques uses sensors/actuators on the structure to progressively monitor the health of the structure with minimal manual intervention. Electrical tomography (ET) is a SHM technique that uses voltage measurements from the surface of the laminate to reconstruct a conductivity map of the structure. Since damage has been shown to modify the conductivity of the laminate, the conductivity map can provide an indirect measure of the damage within the material. Studies have shown the capability of ET to identify macroscale damage due to impact. But, little has been done to quantitatively assess damage using ET. In this work, we present a theoretical framework to link degradation mechanisms occuring at the microscale to the conductivity at the mesoscale through damage indicators. The mesoscale damage indicators are then shown to be intrinsic to the ply. Next, we use the knowledge obtained through mesoscale homogenization to study the detectability of transverse cracks. Last, we show how the mesoscale homogenization participates in regularization of the inverse problem and in the quantitative assessment of the reconstructed conductivity map. This is as such the first step towards turning ET into a viable quantitative health monitoring technique.