Discrete and generalized continuum dynamical models of tetrachiral Cosserat lattices with finite-sized particles

Abstract

Discrete and generalized continuum models of the dynamics of tetrachiral Cosserat lattices consisting of finite-sized particles with complex connections are elaborated. Macrocharacterstics of the chiral lattice are expressed in terms of its microparameters. The dispersion relations of the models are derived. Analysis and comparison of the models are carried out. The obtained single-field long-wavelength and gradient micropolar models provide a good approximation and are applicable to the analysis of the long-wavelength slowly varying deformations. Two-field long-wavelength and gradient micropolar models are elaborated for a one-dimensional case. As distinct from the single-field models, they are constructed using two vector-functions to approximate deformations of the lattice. Six coupled equations of the two-field models are split into two uncoupled systems of equations. One of them coincides with the equations of the single-field models. Thus, the two-field models exhibit the same accuracy as the single-field models for the long-wavelength deformations. Another system of equations describes short-wavelength rapidly varying deformations, for which the single-field models give significant inaccuracy. The two-field models give exact values of frequencies at the edges of dispersion curves in both the long-wavelength and short-wavelength ranges. This can be useful for modeling directional frequency filters in the framework of continuum mechanics.