A standard method, developed by Van der Giessen & Needleman in order to simulate dislocation dynamics in two-dimensional finite domains, was modified so as to account for the effect of dislocations leaving the crystal through a free surface, in the case of arbitrary non-convex domains. The new approach incorporated displacement jumps, across the slip segments of dislocations that had exited the crystal, into finite element analyses carried out to compute the image stresses on the dislocations due to the finite boundaries. This was done in a simple, and computationally efficient, way by embedding the discontinuities in the finite-element solution. This strategy was one often used in numerical simulations of crack propagation in solids. Two examples were given in order to validate and demonstrate the extended model and its implementation within a finite element program.

Dislocation Dynamics in Non-Convex Domains using Finite Elements with Embedded Discontinuities. I.Romero, J.Segurado, J.Llorca: Modelling and Simulation in Materials Science and Engineering, 2008, 16[3], 035008