Aspects of the geometrical description of continuum Bravais monocrystals with many dislocations were considered. A triad of vector fields was first distinguished which constituted a basis for the C∞-module of smooth vector fields tangent to the body. This moving frame defined its anholonomy as well as an intrinsic Riemannian metric of the body. These geometrical entities were then used to define the principal congruence of Volterra-type effective dislocations, and the principal local Burgers vector that were associated with the congruencies. The main features were self-balance equations for dislocations, secondary point defects which were generated by distributions of these dislocations, and a link between the Bianchi classification of 3-dimensional real Lie algebras and the classification of principal local Burgers vectors.

Self-Balance Equations and Bianchi-Type Distortions in the Theory of Dislocations. A.Trzęsowski: International Journal of Theoretical Physics, 2003, 42[4], 711-23