Multiscale Analysis of Laminated Smart Structures with Integrated Piezoelectric Fiber Composite Sensors and Actuators

Alden C. Cook


Piezoelectric materials are capable of altering a structure's response to external stimuli through sensing, actuation, and control. These capabilities have led to their integration into structural systems, forming a diverse class of smart structures. Early investigations of piezoelectric materials in smart structures applications centered on the use of mono-lithic piezoceramic sensors and actuators. However, experience has shown that monolithic piezoceramics are brittle and prone to damage. Furthermore, they have a limited capacity to conform to curved surfaces. In an effort to overcome these limitations, researchers developed flexible piezoelectric fiber composite (PFC) sensors and actuators that consist of aligned piezoceramic fibers embedded in a polymer matrix. PFCs are flexible, durable, and offer the actuation and sensing capabilities of monolithic piezoceramics, making them a practical choice for a wide range of smart structure applications. In order to effectively integrate PFC sensors and actuators into a structural system, it is important to characterize their effective material properties and understand their interaction with the host structure. We present a rigorous multiscale approach based on the asymptotic expansion homogenization (AEH) method to analyze the behavior of laminated smart struc-tures with integrated PFC sensors and actuators. Finite element analysis (FEA) is used to discretize the representative microstructural domain and to determine the effective material properties. The Eshelby-Stroh formalism is applied to satisfy the 3D equilibrium equations at the macroscale and subsequently used to find the average temperature fields, stresses, and electric potential. Finally, interscale transfer operators emerging from the AEH formulation are used in conjunction with FEA to analyze stresses in the fibers and matrix at the microscale. Numerical results for the effective material properties and microscale stresses are compared with results from the literature and show good correlation. Model problems involving PFC shear and extension actuators integrated into fiber-reinforced composite plates are investigated. Although the Eshelby-Stroh formalism can account for arbitrary mechanical, electrical, and thermal boundary conditions, only the last two mentioned are considered here. It is shown that significant differences in stress com-ponents between the two scales can occur, illustrating the necessity of a multiscale analysis when studying laminated smart structures with integrated PFC sensors and actuators. Results demonstrate that the AEH method provides a powerful tool for the comprehensive 3D analysis of laminated smart structures with integrated PFC sensors and actuators.