Generalized continuum models for analysis of one-dimensional shear deformations in a structural interface with micro-rotations

TL;DR

This paper develops and compares generalized continuum models, including two-field and four-field micropolar models, to analyze shear deformations and wave propagation in Cosserat lattice interfaces, capturing both long and short wavelengths.

Contribution

It introduces and evaluates advanced multi-field micropolar models for better analysis of wave behavior and boundary effects in structural interfaces with micro-rotations.

Findings

Two-field models describe both long and short-wavelength waves.

Four-field models improve wave description in the middle of the Brillouin zone.

Models can predict stop band edges and interface filtering properties.

Abstract

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.