Size-Dependent Effects on Dynamic Electromechanical Responses in Dielectric Crystals within Simplified Strain Gradient Elasticity

In this work, we investigate the effect of characteristic length and lattice parameter, associated with microinertia, on internal state variables (displacement, polarization, and electric potential) and constitutive relations (stress, higher-order stress, electric field, and electric field gradient) within a dielectric crystal subjected to gradient of an electric field on its upper surface. To derive the field equations and boundary conditions, we employ the simplified strain gradient theory of elasticity, combined with the variational principle of the electric enthalpy functional and external forces. The resulting boundary conditions are divided into mechanical boundary conditions (including stress vector, higher-order stress vector, and displacement) and electrical boundary conditions (such as electric potential, surface/volume charges, and electric field). The field equations and boundary conditions are then expressed in non-dimensional form. A wave solution approach is used to solve the mathematical model for a half-space occupied by dielectric crystals with cubic symmetry, and the physical quantities are subsequently plotted and analyzed.