Asymmetric mechanical properties in ferroelectrics driven by flexo-deformation effect

The inversion symmetry breaking induced by the strain gradient drives asymmetric mechanical properties in ferroelectrics, which have been evidenced in the asymmetric contact stiffness and asymmetric crack propagation in nanoindentation, as well as asymmetric bending expansion/shrinkage behavior in freestanding ferroelectric oxides. These polarity-dependent asymmetric mechanical properties are closely related to the flexoelectricity, however, the universal mechanism for revealing their common origin is still unclear. In this work, we establish an electromechanical model based on the fundamental flexoelectric framework, and numerically reproduce the asymmetric bending expansion/shrinkage behavior observed experimentally in freestanding ferroelectric oxides. The analysis further reveals that the bending expansion/shrinkage effect is the consequence of the coupling interaction of the flexoelectric electrical field (generated by the strain gradient) and the inverse piezoelectric effect, which contributes to the significant asymmetric bending rigidity. The mechanism underlying the asymmetric bending responses driven by the flexoelectricity is further extended as the flexo-deformation effect, which is revealed to be universal for qualitatively explaining the origin of the asymmetric contact stiffness and the asymmetric crack propagation in ferroelectrics. An unprecedented asymmetric torsion expansion/shrinkage behavior and asymmetric torsional rigidity are also predicted based on the flexo-deformation effect. These findings shed light on the studies about the asymmetric mechanical properties in ferroelectrics, and provide a new approach to design novel devices with asymmetric mechanical functionalities.