  A Lie groupoid, called \textit{second-order non-holonomic material Lie
groupoid}, is associated in a natural way to any Cosserat media. This groupoid
is used to give a new definition of homogeneity which does not depend on a
reference crystal. The corresponding Lie algebroid, called \textit{second-order
non-holonomic material Lie algebroid}, is used to characterize the homogeneity
property of the material. We also relate these results with the previously ones
in terms of non-holonomic second-order $\overline{G}$-structures.
