Mathematical and computational modeling of flexoelectricity

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