Straight Dislocations in Cubic Flexoelectric Solids

Abstract An ultra-high strain gradient field usually exists near dislocations, which breaks the inversion symmetry in dielectrics and induces electric polarization in the material through the flexoelectric effect. Flexoelectricity is an electromechanical coupling phenomenon commonly found in dielectric material, and this flexoelectric effect in anisotropic materials also exhibits complex and significant directional dependencies. In this article, anisotropic strain gradient theory and mathematical methods are used to establish precise constitutive and governing equations for cubic flexoelectric materials. The framework incorporates four constitutive tensors: the second-order reciprocal dielectric susceptibility, the fourth-order elastic tensor, the fourth-order flexoelectric tensor, and the sixth-order elastic tensor. Both open-circuit and short-circuit conditions are considered to define the bounds of the governing equations. By applying Green's function, we address the fundamental nonsingular dislocation problem and derive the displacement and elastic distortion tensors for screw and edge dislocations in cubic flexoelectric materials. Our results not only provide solutions to straight dislocation problems in flexoelectric cubic materials but also can serve as a basis for tuning flexoelectricity in materials by dislocation engineering.