Effective dislocation lines in continuously dislocated crystals. II. Congruences of effective dislocations

Abstract

The notion of a congruence of effective dislocation lines endowed with the nonvanishing local Burgers vector is introduced. Particularly, the class of congruences of principal Volterra-type effective dislocation lines associated with the dislocation densities (tensorial as well as scalar) is distinguished in order to investigate the geometry of continuized defective crystals in terms of these densities. It is shown that effective dislocation lines can be endowed with the dislocation line tension and with a finite self-energy.

arXiv commentKeywords. Anholonomity, crystal surfaces, dislocation density, effective dislocation lines, Frenet formulae, integral manifolds, local Burgers vector, minimal varieties, moving frames, principal congruences, Riemannian space, slip, self-energy, Volterra dislocations