Multi-field modeling of a Cosserat lattice: Models, wave filtering, and boundary effects

•We derived the hierarchy of generalized models for describing shear deformations.•We developed n-field micropolar model to describe staggered boundary effects.•We found spectrum stop bands in a Cosserat lattice.

Various generalized continuum models are developed to analyze the one-dimensional shear deformations of a Cosserat lattice. The original discrete model and the derived continuum models are applied to the analysis of long- and short-wavelength harmonic waves, localized waves, static boundary effects, and the spectrum stop bands in the wave filtering problem. It is found that the conventional single-field and gradient micropolar models are capable of describing the long-wavelength harmonic and localized waves, as well as the static non-staggered boundary effects. However, such models fail to correctly describe the short-wavelength waves, they cannot be used to find the spectrum stop bands and to study staggered boundary effects. On the other hand, the multi-field theory is able to tackle all these problems.