  We develop a theory to represent dislocated single crystals at the mesoscopic
scale by considering concentrated effects, governed by the distribution theory
combined with multiple-valued kinematic fields. Our approach gives a new
understanding of the continuum theory of defects as developed by Kroener (1980)
and other authors. Fundamental 2D identities relating the incompatibility
tensor to the Frank and Burgers vectors are proved under global strain
assumptions relying on the geometric measure theory, thereby giving rise to
rigorous homogenisation from mesoscopic to macroscopic scale.
