Flexoelectric polarization effects in dielectric ceramics depend on the strain gradient and are thus critical in microstructured, bent, indented, stacked, and miniaturized electromechanical devices. The flexoelectric properties of polycrystalline BaTiO$_3$ are determined not only by the numerical value of the flexoelectric coefficients but also by the orientation distribution through which each tensor entry is projected from its crystallographic expression to the coordinate frame of the material. A feasible orientation transfer process is designed for cubic BaTiO$_3$ polycrystals. Using the complete set of tabulated DFT and LDA flexoelectric tensors of BaTiO$_3$ crystals, the four-order flexoelectric tensor is rotated into the specimen coordinate frame, oriented according to the aligned, zero-tilt fiber, tilted-fiber, and isotropic orientations. An entropy-penalty function ensures that the orientation distribution is neither too narrowly peaked nor outside the realistic fabrication range. The tensor-channel transfer capability of an orientation-dependent texture is evaluated based on whether a finite-width tilted fiber texture can yield a stronger thickness-mode coefficient compared with perfectly aligned or isotropic states through the transfer of a predominantly shear-based crystallographic tensor entry. This is indeed the case for both coefficient sets. For the DFT flexoelectric tensor, the value of the thickness-mode coefficient increases from 0.360 nC m$^{-1}$ in the aligned state to 0.954 nC m$^{-1}$ in the tilted fiber texture. For the LDA tensor, the same texture transforms the coefficient from 0.150 nC m$^{-1}$ to -5.088 nC m$^{-1}$, resulting in a 33.9-fold magnitude increase and a flip of polarity. Zero-tilt fiber causes a modulation of in-plane coefficients while leaving the thickness mode unaffected. Isotropic distribution averages the flexoelectric coefficients without retaining any preferential direction. Clearly, for flexoelectric materials, the optimization problem of texture engineering should be framed in terms of tensor-channel transfer.

flexoelectricity,barium titanate,textured ceramics,orientation distribution function,tensor rotation,entropy regularization,polycrystal averaging,shear-channel transfer