Micropolar theory with production of rotational inertia: A farewell to material description

Abstract

This paper takes a new look at micropolar media. Initially the necessary theoretical framework for a micropolar continuum is presented. To this end the standard macroscopic equations for mass, linear and angular momentum are complemented by a recently proposed kinetic equation for the moment of inertia tensor containing a production term. The main purpose of this paper is to study possible forms of this production term and its effects. For this reason two examples are investigated. In the first example we study a continuum of hollow particles subjected to an external pressure and gravity, such that the number of particles does not change. In the second example a continuous stream of matter through a crusher is considered so that the total number of particles will change. In context with these examples it will also become clear that the traditional Lagrangian way of describing the motion of solids is no longer adequate and should be superseded by an Eulerian approach.