Geometrical theory of dislocations in bodies with microstructure

A material body with smoothly distributed microstructure can be seen geometrically as a fibration or, when the symmetry group is specified, as a fiber bundle. Within this very general framework, we present a geometric description of such material bodies in terms of fiber jets. We introduce the notion of fiber frame and construct the corresponding Lie groupoid and fiber <F>G</F>-structure. Then, physical properties of a material body with microstructure as uniformity and homogeneity can be translated in geometrical terms as transitivity for the Lie groupoid or integrability for the fiber <F>G</F>-structure. [Copyright &y& Elsevier]