Flexoelectric effect in dielectrics under a dynamic load

Abstract

Health monitoring of structures can be improved if a more universal two-way electromechanical coupling, the flexoelectric effect, is utilized. It is a coupling between the electric polarization and the strain gradients. In the direct flexoelectricity, the electric polarization is induced by strain gradients, which yield also a finite higher-order stress tensor in the considered phenomenological theory. Because of the size-effect in higher-grade theories of continua, the polarization in piezoelectric solids under a non-uniform strains in nano-sized structures is significantly influenced by flexoelectricity. This effect is substantially enhanced near the crack defects, in regions with large strain gradients. The mixed finite element method (FEM) is developed from the variational formulation of flexoelectric boundary value problems. The C0 continuous approximation is applied independently for both the displacements and displacement gradients. The kinematic constraints between them are satisfied by collocation at some internal points of elements. The developed computational method is applied to general 2D boundary value problems with cracks under a dynamic load. The influence of flexoelectricity on the induced electric potential and the crack opening displacement is investigated.