Continuum Mechanics for Higher Stage Micropolar Materials (2nd Report, Mechanical Balance Laws and Extended Concept of Bimoment)

Mechanical balance laws for micropolar materials stage-2 are discussed on the basis of results of the previous report. The balance equations for mass, force and moment in stage-2 are derived by averaging the balance laws of stage-zero up to stage-2. It is indicated that one more balance law has to be considered, which is those of second-order moment, in order to let the balance equation system be a complete set. The missing equation is gives as the average of the balance equation for the above second-order moment of stage-zero. The authors define a new internal force characterizing the materials of stage-2 and name it “bicouple stress”. This is a second order moment due to the geometric mechanism of multimicrostructures of higher-stage micropolar materials. Furthermore, it is discussed that the bicouple stress extends the concept of bimoment in the theory of thin-walled structures to three-dimensional ones.