On the Homogeneity of Non-uniform Material Bodies

Abstract

Copyright © 2018, arXiv, All rights reserved. A groupoid Ω (B) called material groupoid is naturally associated to any simple body B (see [11, 9, 10]). The material distribution is introduced due to the (possible) lack of differentiability of the material groupoid (see [13, 15]). Thus, the inclusion of these new objects in the theory of material bodies opens the possibility of studying non-uniform bodies. As an example, the material distribution and its associated singular foliation result in a rigorous and unique subdivision of the material body into strictly smoothly uniform sub-bodies, laminates, filaments and isolated points. Furthermore, the material distribution permits us to present a “measure" of uniformity of a simple body as well as more general definitions of homogeneity for non-uniform bodies.MSC Codes 53D17, 18B40, 20L05, 22A22, 74A45, 53Z05