Characteristic distribution: An application to material bodies

Associated to each material body B there exists a groupoid Omega (B) consisting of all the material isomorphisms connecting the points of B. The uniformity character of B is reflected in the properties of Omega (B): beta is uniform if, and only if, Omega (B) is transitive. Smooth uniformity corresponds to a Lie groupoid and, specifically, to a Lie subgroupoid of the groupoid Pi(1) (B, B) of 1-jets of B. We consider a general situation when Omega (B) is only an algebraic subgroupoid. Even in this case, we can cover 13 by a material foliation whose leaves are transitive. The same happens with Omega (B) and the corresponding leaves generate transitive Lie groupoids (roughly speaking, the leaves covering 13). This result opens the possibility to study the homogeneity of general material bodies using geometric instruments. (C) 2018 Elsevier B.V. All rights reserved.