Universal Theoretical Elucidation of Electrobending Deformation in Piezoelectrics

The origin of frequently observed ultrahigh electro-induced longitudinal strain, ranging from 1% to 26%, remains an open question. While recent studies have associated this phenomenon with bending deformation, the underlying mechanisms and the pronounced thickness dependence of the nominal strain have yet to be fully elucidated. Here, we demonstrate that the bending in piezoelectrics can be induced by a nonzero gradient of d_{31} across thickness direction. A scaling law (η_{3,nom}∝L^{2}E_{3}∇_{z}d_{31}/t) is derived to quantify the size dependence, thereby resolving longstanding ambiguities surrounding reported "giant" electrostrains. Simulations reveal that in standard perovskite piezoceramics, such as KNbO_{3}, a 0.69% concentration of oxygen vacancies can induce a 6.3  pC/N variation in d_{31} by suppressing polarization rotation, being sufficient to produce ultrahigh nominal strain in thin samples. Numerous factors, including gradients in defect concentration, composition, and stress, may lead to sufficient inhomogeneity in the distribution of d_{31}, suggesting electrobending may be a widespread phenomenon. This Letter presents a unified framework for understanding electrobending deformation, offering deeper insight into the mechanisms behind abnormally giant electrostrain responses in diverse piezoelectric systems and may encourage new engineering applications.