León, Manuel deJiménez Morales, Víctor Manuel2024-05-202024-05-2020230022-2488https://doi.org/10.1063/5.0159469https://hdl.handle.net/20.500.14468/12560In this paper, we study internal properties of Cosserat media. In fact, by using groupoids and smooth distributions, we obtain three canonical equations. The non-holonomic material equation for Cosserat media characterizes the uniformity of the material. The holonomic material equation for Cosserat media permits us to study when a Cosserat material is a second-grade material. It is remarkable that these two equations also provide us a unique and maximal division of the Cosserat medium into uniform and second-grade parts, respectively. Finally, we present a proper definition of homogeneity of the Cosserat medium, which does not need to assume uniformity. Thus, the homogeneity equation for Cosserat media characterizes this notion of homogeneity.enAtribución-NoComercial-SinDerivadas 4.0 Internacionalinfo:eu-repo/semantics/openAccessartículoContinuum mechanicsGranular materialsLie algebrasDifferential geometryDifferential topologyAlgebraic structuresGeneral topologyGroup theory