Elastic properties of a two-dimensional model of crystals containing particles with rotational degrees of freedom

We consider a discrete two-dimensional model of a crystal with particles having rotational degrees of freedom. We derive the equations of motion and analyze its continuum analog obtained in the long-wave limit. The continuum equations are shown to be the ones of the micropolar elasticity theory. The conditions when the micropolar elasticity equations can be reduced to the equations of conventional elasticity theory are discussed. We show that the rotational degrees of freedom are responsible for the anomalies in the elastic properties of some of the dielectric crystals.