A continuum model of the Peach–Koehler force on dislocations in a slip plane was derived. In order to represent the dislocations, a disregistry across the slip-plane was used whose gradient gave the density and direction of the dislocations. The continuum model was derived rigorously from the Peach–Koehler force acting on dislocations in a region that contained many dislocations. The resultant continuum model could be seen as being the variation of an elastic energy that consisted of a contribution arising from the long-range elastic interactions of dislocations, plus a correction due to the line tension effect.

Continuum Approximation of the Peach–Koehler Force on Dislocations in a Slip Plane. X.Yang: Journal of the Mechanics and Physics of Solids, 2009, 57[4], 728-43