Numerical predictions for the effective properties of flexoelectric composites with spherical inclusion

The direct flexoelectricity in dielectrics, as an electromechanical mechanism coupling electric field and strain gradient, exhibits strong size dependence and structures associated. In the present paper, the effective properties of particulate flexoelectric composites are predicted by the flexoelectric theory. Numerical finite element simulations are realized for representative volume elements (RVE) of the isotropic matrix filled with a spherical flexoelectric inclusion by using mixed variational principle and finite element method (FEM). The elastic fields inside the RVE of different inclusion sizes and volume fractions are studied. The influences of flexoelectricity on the mechanical properties of the composites are discussed. Effective properties of the composites are estimated based on the obtained numerical results. It is shown that flexoelectricity has a great influence on the bulk modulus of composites with a nanoscale inclusion. Due to its size dependence, the flexoelectricity can be neglected in the model with a micron-scale inclusion. At the same time, the selection of length scale will affect the changing trend of effective material properties with volume fraction. Our results suggest that the influence of flexoelectricity on the properties of nanoscale dielectric composites should be emphasized.