On the plane strain problem of dynamical flexoelectric effect in dielectrics subject to Sinc-shaped surface loading

Abstract

Flexoelectricity is a nanoscale phenomenon in dielectric crystals, where the mechanical loads resulting from the first strain gradient shares producing electricity. In this work, we present a numerical investigation for the plane strain problem of the dynamical flexoelectric effect in isotropic dielectrics. A surface loading based on the Sinc function, that is, sincπ(x), with a temporal exponentially decay, is applied to the upper surface of a semi-infinite dielectric crystal. Two cases for the electric potential are considered: (1) Open circuit, in which there is zero charge on the terminals; and (2) Short-circuit, where there is a given value for the potential of the terminals. This type of surface loading is often used in applications such as seismic analysis and electrical engineering, especially signal processing and digital signal processing. Also, it can be used to model other types of dynamic loads, such as wind or wave loads. Furthermore, this setting generates a two-dimensional formulation, known as the plane strain problem. Laplace and Fourier transform techniques are employed for solving the field equations. Suitable numerical techniques are implemented to present the solution to the physical domain. We choose the Strontium Titanate material (SrTiO3) for the two-dimensional simulation. Discussion for the behavior of the dynamical polarization, electric field, electric potential, and stresses is provided in the two-dimensional setting. Effects of the model parameters on electricity generation and behavior are studied.