Boundary element method with internal stresses for the investigation of dislocation-boundary interactions

In the theory of dislocations, most formulas and solutions are for an infinite body. When the body containing dislocations is finite and the boundary effect is significant, the mathematical treatment becomes much more involved and, for most cases, excludes the possibility of closed form solutions. A general numerical method, boundary element method with internal stresses (BEMIS), is developed for investigating dislocation-boundary interactions. In this method, the internal stresses caused by the dislocations are obtained from the infinite body solution, while the boundary element method is used to satisfy the boundary conditions. With BEMIS, the shape of the dislocations, the geometry of the finite body, and the loading conditions may be general, while the boundary may be a free surface or a bi-material interface. The accuracy and versatility of the method are examined through comparison with known closed form solutions.