Suiker A.S.J., Metrikine A.V. and de Borst R. |
Comparison of wave propagation characteristics of the Cosserat continuum model and correspondent discrete lattice models |
International Journal of Solids and
Structures 38(9), 1563-1583, 2001 doi:10.1016/S0020-7683(00)00104-9 |
Summary. A comparison is made between two-dimensional elastic discrete
lattices and a corespondent Cosserat
continuum. First, it is demonstrated how the equations of motion of the Cosserat model can be retrieved from those of a lattice
model. For this purpose, two lattice geometries are elaborated: a 7-cell
hexagonal lattice and a 9-cell square lattice. In both lattices, the
individual cells have two translational spring interactions and a rotational
spring interaction with their neighboring cells.
Secondly, the dispersion relations for the lattice models and the Cosserat continuum model are examined in order to
determine up to which wave length of the deformation field the Cosserat model accurately represents the underlying
discrete micro-structure. The effect of the lattice anisotropy and
inhomogeneity on this accuracy is also discussed. |