A method was proposed in which the dislocation lines were represented in 3 dimensions by the intersection of the zero levels of 2 level set functions. Because the level set method did not discretize nor track directly the individual dislocation-line segments, it could easily handle topological changes which occurred in the microstructure. The dislocation dynamics were not limited to glide along a slip plane, but could also account for 3-dimensional aspects of their motion. Cross-slip occurred naturally, and climb was included by fixing the relative climb and glide mobility. The level set dislocation dynamics method was implemented by using an accurate finite difference scheme on a uniform grid. The examples presented included the motion of dislocation loops under applied and self-stresses (including glide, cross-slip and climb), the intersection of dislocation lines, the operation of Frank–Read sources and dislocations by-passing particles.

A Level Set Method for Dislocation Dynamics. Y.Xiang, L.T.Cheng, D.J.Srolovitz, E.Weinan: Acta Materialia, 2003, 51[18], 5499-5518