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• A procedure is presented for connecting higher-order continuum theories with a discrete lattice model. • Flexoelectric coefficients for higher-order continuum theories, couple stress and strain gradient theories, are determined. • Quantitative comparisons are made to evaluate the performance of the couple stress and strain gradient theories. • In sample problems, the strain gradient theory provides more accurate results than the couple stress theory. 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. [ABSTRACT FROM AUTHOR]

A numerical method for analyzing the mechanical deformation and electric polarization of flexoelectric solids is proposed that considers the electric interactions among flexoelectric solids, electric charges, and their surrounding medium. The proposed method uses finite and boundary elements simultaneously. Finite elements are used to model flexoelectric solids, and boundary elements are applied along the boundary of the solids and an arbitrary surface encompassing the solids and electric charges. To account for the couple stress and flexoelectric terms, a C1 continuous finite element formulation is introduced. Next, a coupled formation between the finite elements and boundary elements is developed. The coupled method provides a converged solution for any system composed of flexoelectric solids and electric charges without prescribing electric boundary conditions on the boundary of solids. Several numerical examples prove that the method is convergent and effective for systems containing multiple solids and electric charges. • A numerical method is presented to analyze flexoelectricity in solids. • The method accounts for the electric interaction among solids, electric charges, and their surrounding medium. • The method can analyze the deformation and polarization of flexoelectric solids. • The coupling requires low additional computational costs and maintains the size of the system matrix. [ABSTRACT FROM AUTHOR]