Remarks concerning forces on line defects

Abstract

This paper covers two different but related topics, concerning applications of two kinds of classical theories to line defects. I start the story with a quotation from Nabarro [1], following his interesting Tribute to J. D. Eshelby, “Eshelby maintained this distinction¹ rigorously. When he calculated the force between parallel disclinations in a nematic liquid crystal and found that “the supposedly configurational force in a nematic is in fact a real force exerted on the core of the dislocation by the surrounding medium”, he was very disturbed, and he circulated the draft of his paper² [2] to many colleagues before publishing it.” I was one of the many and, not long before he died, we happened to attend the same meeting, giving us a chance to discuss the matter. My memory is hardly faultless, but I do remember that I mentioned observations which seemed to me relevant, to be mentioned later, but it was obvious that nothing we said brought us closer to a meeting of minds. The idea that a mechanical force might act on a defect has always seemed reasonable to me, but not to him, so I had trouble understanding what it really was that upset him. Since then, much the same issue has come up in discussions and correspondence with a number of workers, indicating that there is quite a bit of confusion about relevant basic concepts, and that there are differences of opinion about this matter of whether defects can feel those mechanical forces.