  The flexoelectric behaviors of solids under high strain gradient can be
distinct from that under low strain gradient. Using the generalized Bloch
theorem, we investigate theoretically the transversal flexoelectric effects in
bent MgO thinfilms. As a comparison, a centrosymmetric (100) film and a
non-centrosymmetric (111) film are considered. Under bending, the mechanical
responses of both films are linear elastic under low strain gradient but
nonlinear elastic under high strain gradient. In the linear elastic regime, no
internal displacements and thus no polarization contributed from ions are
induced. Only in the nonlinear elastic regime, atoms adopt discernibly large
internal displacements, leading to strong polarization from ions. Because the
internal displacements of atoms of the (111) film are much larger than those of
the (100) film, the obtained flexoelectric coefficient of the (111) film is
also greater than that of the (100) film, revealing strong anisotropy of
flexoelectricity of MgO film. Our results and the employed approach have
important implications for the study of flexoelectric properteis of ionic
solids.
