Computational Modelling of Flexoelectricity: State-of-the-art and Challenges

Flexoelectricity is the polarization of dielectric materials under the gradient of strain. It is electromechanical coupling effect that manifests at micro/nanoscale. Flexoelectricity shares similarity to piezoelectricity, the linear polarization due to strain, but is also essentially different due to two facts. First is the size effects which is more prominent at nanoscale for flexoelectricity and the second the symmetries dislocation is different from piezoelectricity. Besides, under the dynamic loading, flexoelectric materials generate polarization waves having the magnitude proportional to the strain gradient, a phenomenon that is not observed in piezoelectric materials. It has a significant influence on the band-gap and dispersive behavior of meta-materials. Flexoelectricity has shown huge potentials in enabling technology such as self-powered nano devices and writing. Thus in the past decade, it has been intensively studied by various methodologies, theoretically and experimentally, from micro- to macroscopic continuum scale. In this report, we review the modeling of flexoelectricity at different length scales and current challenges remain to be solved. The characterization of flexoelectric coefficients from molecular dynamic simulation to continuum model remains the gap that needs to be bridged in a multiscale framework between different length-scales in flexolectric-based device modeling.