  A groupoid $\Omega \left( \mathcal{B} \right)$ called material groupoid is
naturally associated to any simple body $\mathcal{B}$. The material
distribution is introduced due to the (possible) lack of differentiability of
the material groupoid. 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.
