The topological theory of defects was applied to a simple model, for a crystalline microstructure, which was suitable for the study of elastic crystals. The model was obtained by restricting the range, of the map which described the local lattice, to the neighborhood of a given reference Bravais lattice. It was shown that the topological structure of the chosen set of points was sufficiently rich to permit the description of disclinations (related to point group symmetries) and twins (related to non-rotational symmetries), but not the treatment of defects which corresponded to simple shear symmetries.

P.Cermelli, E.Mazzucco: Physica D, 1996, 99[2-3], 350-9