The behavior of a Bravais crystal under volume-conserving plastic deformation was considered. It was noted that such a crystal was a metric solid which permitted the measurement of lengths by counting atomic steps and applying Pythagoras’ law. When the lattice spacing was imagined to be made smaller and smaller, the above remained true. If the shrinking were done while allowing for conservation of the local dislocation content, the distance between the scaled-down dislocations (measured in scaled-down atomic distances) tended to infinity while the dislocations remained in the so-called continuum crystal. Frank’s definition for the dislocation remained valid under this transformation. Because the numbers and types of discrete dislocations could be determined, the dislocation density could be introduced as an explicit state quantity in the continuum crystal. Explicit state quantities were defined to be those which entered into the energy expression explicitly as independent variables. In normal structureless continua, dislocations (as defined by Burgers) were not state quantities. Thus, these dislocations did not appear as dynamical variables in the relevant field theory. Therefore, the mechanical theory of normal structureless continua was not suitable in situations where the internal mechanical state underwent appreciable change.

Dislocations in Crystals and in Continua. E.Kroner: International Journal of Engineering Science, 1995, 33[15], 2127-35