  This paper develops a geometrical model of dislocations and disclinations in
single crystals at the mesoscopic scale. In the continuation of previous work
the distribution theory is used to represent concentrated effects in the defect
lines which in turn form the branching lines of the multiple-valued elastic
displacement and rotation fields. Fundamental identities relating the
incompatibility tensor to the dislocation and disclination densities are proved
in the case of countably many parallel defect lines, under global 2D strain
assumptions relying on the geometric measure theory. Our theory provides the
appropriate objective internal variables and the required mathematical
framework for a rigorous homogenization from mesoscopic to macroscopic scale.
