Comparison of wave propagation characteristics of the Cosserat continuum model and corresponding discrete lattice models

A comparison is made between two-dimensional elastic discrete lattices and a corresponding Cosserat continuum. Firstly, it is demonstrated how the equ ations of motion of the Cosserat model can be retrieved from those of a lat tice model. For this purpose, two lattice geometries are elaborated: a 7-ce ll hexagonal lattice and a 9-cell square lattice. For both lattices, the in dividual cells have two translational spring interactions and a rotational spring interaction with their neighbouring cells. Secondly, the dispersion relations for the lattice models and the Cosserat continuum model are exami ned in order to determine up to which wavelength of the deformation held th e Cosserat model accurately represents the underlying discrete micro-struct ure. The effect of the lattice anisotropy and inhomogeneity on this accurac y is also discussed. (C) 2001 Elsevier Science Ltd. All rights reserved.