A unified model for the dynamical flexoelectric effect in isotropic dielectric materials

The present work proposes a unified model for studying the dynamical flexoelectricity by including effects of the micro-inertia, the dynamical polarization, and the dynamical flexocoupling between displacement and polarization upon the mechanical and electrical states of the dielectric material. The mathematical description is presented in the framework of strain gradient elasticity. Using the variational technique for internal energies and external forces, the governing equations are derived with their concomitant boundary conditions for homogeneous anisotropic flexoelectric materials. The focus is on the study of the effects of such dynamical sizedependent and dynamical flexocoupling tensor on the class of centrosymmetric isotropic dielectric materials, which referred to as the flexoelectric effect, by means of the integral transform technique. A one-dimensional application is presented for a semi-infinite flexoelectric material. The solution is obtained using the integral transform method, precisely, the Laplace transform. The strontium titanate (STO) is chosen for the numerical simulation. It is emphasized that the size-dependent factor diminishes the dynamical wave feature of the response variables. Otherwise, the flexocoupling parameter is found to play a key role in polarization production inside the dielectric medium.