  Generalized continuum models for describing one-dimensional shear
deformations of a Cosserat lattice are considered and their application to
describing of structural effects essential for interfaces are discussed. The
two-field long-wavelength micropolar model and its gradient and four-field
generalizations are obtained and compared to the single-field conventional and
gradient micropolar models. The single-field models can be applied to the
analysis of long-wavelength deformations, but it does not describe
short-wavelength waves and boundary effects. It is demonstrated that the
two-field models describe both long-wavelength and short-wavelength harmonic
waves and localized deformations and may be used in order to find stop band
edges and to study the filtering properties of the interface. The two-field
models make it possible to describe not only exponential but also
short-wavelength boundary effects and evaluate degree of its spatial
localization. The four-field model improves the two-field model in the
description of the waves with wavenumbers in the middle part of the first
Brillouin zone and may be useful to specify stop band edges in the case when
minima/maxima of the dispersion curves belong to this region. The reported
results are especially important for modeling of structural interfaces in the
case when the length of localization is comparable with the interface
thickness.
