Determination of flexoelectric coefficients of higher-order continuum theories from CsCl lattice model

Flexoelectricity is an electromechanical coupling phenomenon between inhomogeneous deformation and electric polarization. The classical theory, which relies on the strain, is insufficient for representing flexoelectricity. Instead, a higher-order continuum theory that employs a measure capable of expressing local inhomogeneous deformation is necessary. In the present work, we concatenate higher-order continuum theories with a CsCl lattice structure consisting of charged particles and determine the resulting constitutive coefficients for higher-order continuum theories. First, we derived continuum internal energy density functions for dielectrics from the conservation laws. We consider two different higher-order continuum theories: coupled stress and strain gradient theories. Second, we present a procedure for determining the coefficients of higher-order continuum theories by using a discrete lattice model under the assumption that the internal energies of the lattice and continuum models are the same for identical deformations. To validate the coefficients, three sample problems are examined by presenting their analytical solutions. The results of sample problems demonstrate that the two higher-order theories can provide quantitative information about the size and flexoelectric effects. In particular, the strain gradient theory predicts the deformation of the lattice structure more accurately.