A unified six‐dimensional treatment of elastic green's functions and dislocations

Dislocations together with forces in infinite elastic media are treated in a six‐dimensional formalism. Expressions for the displacement fields of point sources (i.e. the elastic Green's function), of elementary dislocation loops and of straight dislocations and line forces are given both for the static case and for uniform motion. The connection with similar expressions given by others is shown. The relations between matrices, eigenvectors, and eigenvalues are studied. The formalism developed simplifies the evaluation of perturbation expansions and derivatives. It is shown that the same eigenvalue problem appears for different sources suitably chosen.