Key points are not available for this paper at this time.
Higher-order two-way electromechanical coupling between strain gradients and electric field, known as flexoelectricity, has a strong influence on the micro- and nanoelectromechanical devices characterization as it is highly pronounced on smaller scales. Flexoelectricity in dielectrics and piezoelectrics has been well analyzed recently, however, its influence on the behavior of ferroelectric materials has not been explored yet. On the one hand, the current study can be seen as an expansion of ferroelectric material behavior towards higher-order electromechanical coupling. On the other hand, it can be treated as an advancement of flexoelectricity to non-linear material behavior, including inherent residual stresses and polarization. Either way of thinking is equally justified and leads to a substantial advancement in material modeling that incorporates small scales and strong electromechanical loading that drives the ceramics out of the linear response domain. For the numerical implementation, the mixed FEM is successfully employed. This involves the formulation from scratch of a three-dimensional mixed FE for flexoelectricity in dielectrics/piezoelectrics. After its successful verification, the micromechanical ferroelectric switching model is additionally implemented into the mixed FE. Initial investigations involve single and polycrystalline representative volume element simulations, which enable the analysis of the altered hysteresis loops. Following this, novel simulations of the truncated pyramid problem for flexoelectricity + ferroelectricity are performed. The introduced fully coupled, multi-scale, mixed FEM-based electromechanical model brings insights into the combined impact of the first-order nonlinear (ferroelectricity) and higher-order (flexoelectricity) responses.
Serrao et al. (Mon,) studied this question.