Lie groupoids and algebroids applied to the study of uniformity and   homogeneity of material bodies
  A Lie groupoid, called \textit{material Lie groupoid}, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called \textit{material algebroid}, is used to characterize the uniformity and the homogeneity properties of the material. The relation to previous results in terms of $G-$structures is discussed in detail. An illustrative example is presented as an application of the theory. 
V. M. Jim\'enez, M. de Le\'on, M. Epstein
math.DG