It was pointed out that, in dislocation theory, most formulae and solutions applied to infinite bodies. However, when a body which contained dislocations was finite and the boundary effect was significant, mathematical treatment became much more difficult and this usually precluded closed-form solution. A general numerical method (boundary element method with internal stresses) was developed here for the investigation of dislocation-boundary interactions. In this method, internal stresses which were caused by dislocations were deduced from infinite-body solutions, while the boundary element method was used to satisfy boundary conditions. The shape of the dislocations, the geometry of the finite body and the loading conditions could be very general, while the boundary could be a free surface or a bi-material interface.

Boundary Element Method with Internal Stresses for the Investigation of Dislocation-Boundary Interactions. X.J.Xin, K.Kollu, R.H.Wagoner: Materials Science and Engineering A, 2001, 309-310, 520-3