This paper
Hirth, J.P. A brief history of dislocation theory.
Metall Mater Trans A 16, 2085ā2090 (1985).
https://doi.org/10.1007/BF02670413
has this paragraph
Brown,52while considering magnetic properties of dis- locations, originated the concept of smearing discrete dislocations into a continuous array of infinitesimal dis- locations. This method has resulted in connections with powerful methods of mathematics but describes properties of the net dislocation density and has some problems in uniqueness and the description of arrays of dislocations of opposite sign. In early work, Nye53described the connec- tion between the net dislocation density tensor and the lat- tice curvature. Kondo54and Bilby, Bullough, and Smith55 showed that the Cartan torsion of space is the continuum equivalent of the dislocation, with the Cartan circuit closely related to the Burgers circuit.56The latter authors used the continuum description to derive the geometric properties of grain boundaries. Kr/Sners7 developed the concept of the incompatibility, proportional to derivatives of the dislocation density, and descriptions of the elastic fields in terms of it. Further advances are discussed in several reviews. 57.58,59
and refs 52-59
52. W.E Brown: Phys. Rev., 1941, vol. 60, p. 139.
53. J. E Nye: Acta MetaU., 1953, vol. 1, p. 153.
54. K. Kondo: RAAG Memoirs of the Unifying Study of the Basic Prob-
lems in Engineering Sciences by Means of Geometry, Gakujutsu Buuken Fukyu-Kai, Tokyo, 1955, vol. I, p. 453; also see Ref. 46, p. 761.
55. B.A. Bilby, R. Bullough, and E. Smith: Proc. Roy. Soc. London, 1955, vol. A231, p. 263.
56. E. KriJner: in Dislocation Modeling of Physical Systems, M.F. Ashby, R. Bullough, C. S. Hartley, and J. P. Hirth, eds., Pergamon, Oxford, 1981, p. 285.
57. E. Kr/Sner: Ergeb. angew. Math, 1958, vol. 5, p. 1.
58. E. Cosserat and F. Cosserat: Theorie des Corps Deformables,
Herman, Pads, 1909.
59. Mechanics of Generalized Media, E. KriSner, ed., Springer, Berlin,
1968.
) need of some reference that treats the theory of dislocations in crystal with a mathematical emphasis (i.e. tensors); specifically, pertaining to Burgers' vectors and the strain response to applied stress in crystals containing dislocations. Does such a reference exist?