Characteristic distribution: An application to material bodies.

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