Size-dependent bending of an electro-elastic bilayer nanobeam due to flexoelectricity and strain gradient elastic effect

A size-dependent bending model of an electro-elastic bilayer nanobeam including an isotropic dielectric layer and an elastic layer is established based on the flexoelectricity theory and the strain gradient theory. The governing equations and boundary conditions are derived from electric enthalpy variation principle with consideration of electrostatic force. The static bending problems of bilayer cantilever under closed and open circuit conditions are solved to show the size-dependency of the flexoelectric effect in both direct and converse flexoelectric processes. Numerical results demonstrate that both the strain gradient elastic effect and the flexoelectric effect significantly influence the deflection of the bending cantilever when the beam thickness is comparable to the material length scale parameters. Due to the flexoelectricity, sharp gradients of the electric field and polarization field arise near the surfaces, which differs greatly from the uniform field in the classical theory. In addition, the electric potential generated in the direct flexoelectric process and the deflection generated in the converse flexoelectric process exhibit obvious size-dependency.