Lie groupoids and algebroids applied to the study of uniformity and homogeneity of Cosserat media

Abstract

A Lie groupoid, called second-order non-holonomic material Lie groupoid, is associated in a natural way to any Cosserat medium. This groupoid is used to give a new definition of homogeneity which does not depend on a material archetype. The corresponding Lie algebroid, called 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 obtained ones in terms of non-holonomic second-order [Formula: see text]-structures.