Abstract
The geometrical theory of continuous distributions of dislocations traditionally neglects the dependence of a distribution of dislocations on the existence of point defects created by this distribution (e.g., due to intersections of dislocation lines). In this paper the influence of such point defects on metric properties of the continuized dislocated Bravais crystalline structure is assumed to be isotropic. The influence of the point defects on the distribution of dislocations is then modeled by treating dislocations as those located in a conformally flat space. This approach leads (among others) to new results concerning the geometry of glide surfaces.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Barut, R., and Rączka, R. (1977).Theory of Group Representations and Applications, PWN, Warsaw [in Polish].
Bilby, B. A., Bullough, R., Gardner, L. R. T., and Smith, E. (1958).Proceedings of the Royal Society A,244, 538.
Bullough, R., and Newman, R. (1970).Reports on Progress in Physics,33, 101.
Davini, C., and Parry, G. P. (1991).Proceedings of the Royal Society A,432, 341.
Eisenhart, L. P. (1964).Riemannian Geometry, Princeton University Press, Princeton, New Jersey.
Fagundes, H. V. (1991).General Relativity and Gravitation,2, 199.
Frank, F. C., and Steeds, J. W. (1975). InThe Physics of Metals, Vol. 2, P. B. Hirsh, ed., Cambridge University Press, Cambridge.
Gołąb, S. (1966).Tensor Calculus, PWN, Warsaw [in Polish].
Hull, D., and Bacon, D. J. (1984).Introduction to Dislocations, Pergamon Press, Oxford.
Kröner, E. (1984). InDislocations in Solids, Some Recent Advances, K. Markensoff, ed., American Society of Mechanical Engineers, New York.
Kröner, E. (1985). InDislocations and Properties of Real Materials, Institute of Metals, London.
Kröner, E. (1986).Zeitschrift für Angewandte Mathematik und Physik,66, T.284.
Kröner, E. (1990).International Journal of Theoretical Physics,11, 1219.
Oding, I. A. (1961).Theory of Dislocations in Metals, PWT, Warsaw [in Polish].
Orlov, A. N. (1983).Introduction to the Theory of Defects, Moscow [in Russian].
Trzęsowski, A. (1989).International Journal of Theoretical Physics,5, 543.
Trzęsowski, A. (1993).Reports on Mathematical Physics,1, 71.
Trzęsowski, A. (1994).International Journal of Theoretical Physics,4, 1059.
Trzęsowski, A. (1995).Progress of Physics,43, 1.
Yano, K. (1955).The Theory of Lie Derivatives and its Applications, North-Holland, Amsterdam.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Trzęsowski, A. On the isotropy of continuized dislocated crystals. I. The isotropic lattice distortion. Int J Theor Phys 36, 177–191 (1997). https://doi.org/10.1007/BF02435780
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02435780