On smectic-A liquid crystals in an electrostatic field

Smectic-A liquid crystals are layered anisotropic materials with anisotropic dielectric features. In this paper we propose a non-linear model describing the static finite deformations induced in a smectic-A by an electrostatic field. In the classical approach, the electric field is considered partially coupled with the mechanical system in the sense that it can induce layer distortions, but it is not affected by these distortions. In our model, the momentum balance equation is fully coupled with Maxwell's electrostatic equations. We study the phase transition induced by an electric field for a simple planar cell of smectic-A in two undistorted configurations: a homeotropic texture and a bookshelf geometry, both with strong anchoring boundary conditions.