Continuum Mechanics for Higher Stage Micropolar Materials (1st Report, Kinematics)

A concept of higher stage polar materials, proposed in the previous report, has extended the usual micropolar theory to the n-stage. It is necessary to construct a generalized continuum mechanics for the higher-stage micropolar materials on the basis of this concept. In the present paper, the kinematics for micropolar materials of stage-2 is discussed as preliminary to this. In order to express the complicated geometric mechanism due to the multimicrostructure of higher stage polar materials, the strain gradient theory is introduced into micropolar theory. The results obtained here are summarized as follows. Micropolar materials of stage-2 have not only the degrees of freedom of displacement and microrotation, which are assigned to the usual micropolar materials of stage-1, but also one of microtorsional rotation. Additionally, transport theorem for each stage is derived.