On the Theories of Plates Based on the Cosserat Approach

The classical isotropic linear elastic material behavior is presented by two material parameters, e.g., the Young's modulus and the Poisson's ratio, while the Cosserat continuum is given by six material parameters. The latter continuum model can be the starting point for the deduction of the governing equations of the Cosserat plate theory via a through-the-thickness integration. In contrast, the basic equations of the Cosserat plate theory can be established applying the direct approach. It can be shown that both systems of equations are similar in the main terms. The assumed identity of both systems results in consistent stiffness parameters identification for the two-dimensional theory based on the direct approach and, in addition, in some constraints. Using the experimental results of Lakes, one can show in which cases the additional material properties coming from the tree-dimensional Cosserat material model have a significant influence on the stiffness parameters.