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Isotropic Limiting Behaviour of the Six‐Dimensional Formalism of Anisotropic Dislocation Theory and Anisotropic Green's Function Theory. I. Sum Rules and Their Applications
Author(s) -
Nishioka K.,
Lothe J.
Publication year - 1972
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.2220510225
Subject(s) - isotropy , anisotropy , eigenvalues and eigenvectors , limiting , dislocation , limit (mathematics) , mathematical analysis , formalism (music) , mathematics , physics , quantum mechanics , condensed matter physics , mechanical engineering , art , musical , engineering , visual arts
The isotropic limiting behaviour of the six‐dimensional anisotropic dislocation theory of Stroh [1] is studied. By means of certain sum rules, it is possible to go to the limit of isotropy without a detailed study of the degeneracies arising for the eigenvalues and the eigenvector system. The sum rules combined with the perturbation expressions of Malkn and Lothe [2] also readily give expansions for dislocation energy factors and Green's functions to the first order in the deviation from isotropy.