Deformation measures of micropolar theory in spatial and material description – A review

In this paper we present a review of some of the foundations of micropolar continua. The focus is initially on the classical representation of fields in spatial or material description. We shall remind the reader that traditionally both are based on the notion of the indestructible material particle. We will give reasons why these traditional concepts may fail, namely if we wish to study more complex processes, such as agglomeration or crushing of matter. As a way out, we will present a suitable extension, which we call true spatial description. We shall also demonstrate that the classical twofold approach can lead to serious misunderstandings that may result in unnecessary scientific controversies. Further attention is paid to the various deformation measures that are encountered in the literature on micropolar materials. It will be discussed under which circumstances which one should preferably be used. In this context the kinetic equation for the microinertia tensor deserves particular attention: it was recently extended by a production term. This additional feature can be used to describe processes in matter associated with micromorphological change, for example during crushing and milling of substances. Here a continuum description in terms of material, indestructible particles is no longer possible, and true spatial notation becomes a must.