Micropolar media with structural transformations . theory illustated by an example problem


This paper is concerned with a model for an extended theory of micropolar media. The extension concerns the balance for the tensor field of the moment of inertia, which in contrast to previous theories contains a production term. This term becomes important if the micropolar material undergoes structural changes. In the present case we consider an assemblage of hollow spheres, which due to a transient temperature field contract or expand. This leads to a true field for the tensor of the moment of inertia varying in space and time. For this situation the production term can be calculated numerically. In addition, the temporal and spatial change of the macroscopic inertia field influences rotational motion. Based on a numerical solution for the balance of spin we study the evolvement of angular velocity in space and time. The importance of the presence of a volume couple density is stressed and its physical realization will be discussed.