We try to characterize states of a plastically deformed material from first principles. There is a hierarchy of scales, in which the description of the material, e.g. a metal, changes. On the atomic scale it is an imperfect lattice. On the mesoscopic scale it is a fibre bundle (with affine or generalized affine connection) with defects or ends, i.e. the dislocations discovered by V. Volterra. Going to the next level there are two competing descriptions: The Cosserath theory and the non-Riemannian geometry proposed by K. Kondo and E. Kröner. We are trying to prove in a rigorous way, based on energetic consideration, that a modified Cosserath theory provides the correct answer. Important tools are the rigidity estimates by Friesecke, James, Müller and by Müller, Scardia, Zeppieri. (joint work with L. Mugnai, J. Wohlgemuth, G. Lauteri)