On a ordering of area tensor elements orientations in a micropolar continuum immersed in an external plane space

Abstract

The paper deals with the problems of ordering the reper orientations for a micropolar continuum immersed in an external plane space. Based on the concept of an elementary tensor volume (area) \(M\)-cells, an algorithm for comparing and matching external spatial orientations of \(M\)-cells is proposed. The process of continuous transfer of reper directions associated with a \(M\)-cell is considered. As a result, we can talk about the orientation of micropolar continuum itself and its boundary. The oriented continuum plays an important role in micropolar elasticity. This is especially true for the theory of hemitropic elastic media. The pseudotensor formulation of Stokes' theorem is discussed.