Mathematical and computational modeling of flexoelectricity

We first revisit the mathematical modeling of the flexoelectric effect in the context of continuum mechanics at infinitesimal deformations. We establish and clarify the relation between the different formulations, point out theoretical and numerical issues related to the resulting boundary value problems, and present the natural extension to finite deformations. We then present a simple B-spline based computational technique to numerically solve the associated boundary value problems, which can be extended to handle unfitted meshes, hence allowing for arbitrarily-shaped geometries. Several numerical examples illustrate the flexoelectric effect in simple benchmark setups, as well as in new flexoelectric devices and metamaterials engineered for sensing or actuation. Published under an exclusive license by AIP Publishing.

Automated summary

This paper revisits the mathematical modeling of the flexoelectric effect in the context of continuum mechanics and presents a computational technique based on B-splines to solve the associated boundary value problems. Numerical examples demonstrate the flexoelectric effect in various geometries and its application in new flexoelectric devices.