Multi-field Continuum Theory for Medium with Microscopic Rotations

Abstract

We derive the multi-field, micropolar-type continuum theory for the two-dimensional model of crystal having finite-size particles. Continuum theories are usually valid for waves with wavelength much larger than the size of primitive cell of crystal. By comparison of the dispersion relations, it is demonstrated that in contrast to the single-field continuum theory constructed in our previous paper the multi-field generalization is valid not only for long but also for short waves. We show that the multi-field model can be used to describe spatially localized short- and long-wavelength distortions. Short-wave external fields of forces and torques can be also naturally taken into account by the multi-field continuum theory.