Peach-Koehler theory is implemented to simulate the motion of three-dimensionally interacting dislocations, located on various glide planes and having any allowed Burgers vector. The self-interaction is regularized by a modified Brown procedure, which remains stable and loses accuracy in a well-controlled manner as atomic dimensions are approached. The method is illustrated by applying it to several problems involving interacting dislocations in an fcc slip system. The strong interaction of two dislocations on intersecting glide planes is investigated with a view towards developing a set of rules to describe the outcome of such interactions. The effect of Frank-Read sources in relaxing a strained layer are illustrated, both for sources on parallel and on intersecting glide planes.
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