Isotropic Limiting Behaviour of the Six‐Dimensional Formalism of Anisotropic Dislocation Theory and Anisotropic Green's Function Theory. I. Sum Rules and Their Applications

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.