A flexoelectric actuator model with shear-lag and peel stress effects

Flexoelectric materials are being extensively studied in recent years for potential sensing, actuation, energy harvesting and structural health monitoring applications. However, no analytical model exists in the literature to predict the stress transfer between a flexoelectric transducer and the host structure, considering bonding compliance. In this article, we present an analytical model for the interfacial stresses and deformations of flexoelectric patch actuator(s) bonded to an isotropic host plate considering both shear-lag and peel stress effects at the interface(s). The model is valid for both piezoelectric and flexoelectric effects. The system's one-dimensional governing equations are derived consistently from the three-dimensional equations for linear dielectric solids obtained using the bulk electric Gibbs energy density function and extended Hamilton's principle. The transducer and substrate, modelled as classical Kirchhoff plates, undergo both extension and bending deformations. The formulation produces a seventh-order differential equation for the interfacial shear stress, which is solved analytically, satisfying all boundary conditions. The solution is validated by comparing with the available results for piezoelectric actuators with a non-rigid interface and those of flexoelectric actuators based on the pin-force-moment model assuming a rigid interface. Detailed numerical studies are presented to show the effect of the plate, actuator and adhesive parameters on the interfacial stresses and deformations. Finally, the size effect of the actuators at the micro-scale is illustrated.