DOIAbstract
The concept of material distribution is introduced as describing the geometric material structure of a general non-uniform body. Any smooth constitutive law is shown to give rise to a unique smooth integrable singular distribution. Ultimately, the material distribution and its associated singular foliation result in a rigorous and unique subdivision of the material body into strictly smoothly uniform components. Thus, the constitutive law induces a unique partition of the body into smoothly uniform sub-bodies, laminates, filaments and isolated points.This work was supported by MINECO Grants MTM2013-42-870-P and the ICMAT Severo Ochoa projects SEV-2011-0087 and SEV2015-0554. V.M.J. wishes to thank MINECO for a FPI-PhD Positio