Piezoceramic fiber composite (PFC) actuators and sensors offer many advantages over conventional monolithic piezoceramic devices. Conformable, durable and, when equipped with interdigitated electrodes (IDEs), more responsive than regular monolithic devices, PFCs promise to revolutionize the application of piezoelectric materials. Developed by the NASA-Langley Research Center, the Macro-Fiber Composite (MFC) actuator and sensor is the most sophisticated PFC device yet invented. With superior qualities among PFCs in performance, behavior repeatability and manufacturability, the MFC has spawned great interest in the commercial and academic community as a tool in multitudinous engineering applications.

While the MFC's characteristics render it a singularly useful device, limited characterization and modeling research on the MFC exists. Empirically designed and assembled, the MFC is poorly understood, especially in terms of its underlying operating principles, its dependence on design parameters and its electrical properties. The majority of published MFC studies focus on experimental quantification of MFC mechanical and actuation properties, and the research that attempts to model the MFC relies totally on finite element analysis. Published works widely assume that analytical models of the MFC are totally impossible.

Rectifying gaps in the current body of MFC research, this study presents the first accurate analytical model of the static electrical field properties of the MFC. Implementing the techniques of conformal mapping, a branch of complex analysis, the following chapters derive a closed-form, exact analytical solution describing the electrical potential field and electrical field of the MFC's dual-IDE structure. Based on the conformal mapping solution for the MFC's electrical field, the electrical field of the commercially available MFC is examined and analyzed, introducing an intuitive knowledge of the MFC's operation. Demonstrating the utility of this solution in modeling the MFC, this work also predicts the capacitance and induced strain properties of a continuum of potential MFC designs and offers final suggestions on improving the current commercial MFC design. After establishing the theoretical underpinnings of the analytical MFC model, this report derives the conformal mapping solutions for the MFC, discusses the computational application of the resulting equations and then presents the results of numerical analyses executed using the new analytical model.