Micropolar theory from the viewpoint of mesoscopic and mixture theories

Аннотация

This paper takes a nontraditional look at micropolar media. It emphasizes the idea that it may become necessary to abandon the concept of material particles if one wishes to describe micropolar matter in which structural changes or chemical reactions occur. Based on recent results presented by Ivanova and Vilchevskaya (2016) we will proceed as follows. First we shall summarize the theory required for handling such situations in terms of a single macroscopic continuum. Mne of its main features are new balance equations for the local tensors of inertia containing production terms. The new balances and in particular the productions will then be interpreted mesoscopically by taking the inner structure of micropolar matter into account. As an alternative way of understanding the new relations we shall also attempt to use the concepts of the theory of mixtures. However, we shall see by example that this line of reasoning has its limitations: A binary mixture of electrically charged species subjected to gravity will segregate. Hence it is impossible to use a single continuum for modeling this kind of motion. However, in this context it will also become clear that the traditional Lagrangian way of describing motion of structurally transforming materials is no longer adequate and should be superseded by the Eulerian approach.