Bending of a Flexoelectric Semiconductor Plate

We study electromechanical responses of a flexoelectric semiconductor plate in bending under mechanical loads. A two-dimensional theory for classical bending without shear deformation is derived from the three-dimensional macroscopic theory of flexoelectric semiconductors. A simple solution is obtained for pure bending. A combination of physical and geometric parameters is introduced as a measure of the strength of the coupling between the mechanical load and the redistribution of charge carriers. A trigonometric series solution is obtained for a simply supported rectangular plate under a local normal mechanical load, which shows concentration of mobile charges and the formation of electric potential barriers near the loading area. The results are fundamental to the mechanical manipulation of charge carriers in these plates. We also analyze the buckling of a simply supported rectangular plate under in-plane compressive forces. A series of buckling loads and modes are obtained. Numerical results show that flexoelectric coupling exhibits a stiffening effect and increases the buckling load, while semiconduction weakens the flexoelectric stiffening. The distributions of mobile charges in the first few buckling modes are presented.