A new technique for the modelling of multiple dislocations based upon introducing interior discontinuities was presented. In contrast to existing methods, the superposition of infinite domain solutions was avoided; interior discontinuities were specified on the dislocation slip surfaces and the resulting boundary value problem was solved by a finite element method. The accuracy of the proposed method was verified and its efficiency for multi-dislocation problems was illustrated. Bounded core energies were incorporated into the method through regularization of the discontinuities at their edges. Though the method was applied to edge dislocations here, its extension to other types of dislocations was straightforward.

A New Fast Finite Element Method for Dislocations Based on Interior Discontinuities. R.Gracie, G.Ventura, T.Belytschko: International Journal for Numerical Methods in Engineering, 2006, 69[2], 423-41