Micropolar nematic model for polarized liquid crystals

A micromorphic electroelastic model for polarized liquid crystals is proposed on the basis of a representation of electric multipoles in terms of microdeformation. Nematic liquid crystals are modeled as micropolar continua endowed with intrinsic electric dipole and quadrupole. A nonlinear dimensionless problem for a homogeneous nematic layer is formulated and solved numerically. The existence of a threshold electric potential is discussed, and the corresponding linearized system is also obtained to compare results on small values of deformation and electric field. Differently from common results of the classical continuum approach, asymmetric deformations and electric potentials within the layer are obtained due to the occurrence of non-null intrinsic quadrupole.