Ellipsoidal Inclusions in Flexoelectric Solids

Abstract The flexoelectric effect, characterized by the induction of electric polarization by strain gradients, exhibits a remarkable size dependence. This makes flexoelectricity highly relevant for nanoscale electromechanical systems. Inevitably, flexoelectric solids, like all materials, are susceptible to various types of defects. These defects significantly influence the local electromechanical coupling phenomena, thereby affecting the performance of flexoelectric materials. This study investigates ellipsoidal inclusions in flexoelectric solids, a fundamental and classical defect type. We present Green’s functions for flexoelectricity, which is the basis for formulating the eigen deformation problem within flexoelectricity theory. We then derive the expressions for strain dilatation, electric potential, and polarization magnitude under a constant eigenstrain dilatation scenario, which allows us to effectively address the ellipsoidal inclusion problem in flexoelectric solids. The investigation then extends to different ellipsoidal inclusions, shedding light on their distinctive shape and size effects. The insights gained from this study provide perspectives on the potential failure mechanisms in defective flexoelectric solids and lay a theoretical foundation for the design of nanoscale flexoelectric systems.