Characteristic distribution: An application to material bodies

Associated to each material body B there exists a groupoid ΩB consisting of all the material isomorphisms connecting the points of B. The uniformity character of B is reflected in the properties of ΩB: B is uniform if, and only if, ΩB is transitive. Smooth uniformity corresponds to a Lie groupoid and, specifically, to a Lie subgroupoid of the groupoid Π1B,B of 1-jets of B. We consider a general situation when ΩB 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 ΩB 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.