Micropolar Theory with Production of Rotational Inertia: A Rational Mechanics Approach

Abstract

The aim of this paper is a review on recently found new aspects in the theory of micropolar media. For this purpose the necessary theoretical framework for a micropolar continuum is initially presented. Here the standard macroscopic equations for mass, linear and angular momentum, and energy are extended in two ways. First, the aspect of coupling linear and angular rotational kinetic energies is emphasized. Second, the equations are complemented by a recently proposed kinetic equation for the moment of inertia tensors containing a production term. We then continue to explore the possibilities of this new term for the case of micropolar media encountering a change of moment of inertia during a thermomechanical process. Particular emphasis is put on the general form of the production of moment of inertia for a transversally isotropic medium and its potential to describe, for example, structural changes from a transversally isotropic state to an isotropic one. In order to be able to comprehend and to study the influence of the various material parameters the production term is interpreted mesoscopically and various other examples are solved in closed form. Moreover, in context with the presented example problems it will also become clear that the traditional Lagrangian way of describing the motion of solids might sometimes no longer be adequate and must then be replaced by a Eulerian approach.