A thermodynamics-based variational method was developed in order to derive equations of motion for 3-dimensional interacting dislocation loops. The approach was suitable for the investigations of plastic deformation at the mesoscopic scale by direct numerical simulation. A fast-sum technique for the determination of the elastic-field variables of dislocation ensembles was used to calculate the forces which acted upon the generalized coordinates of arbitrarily curved loop segments. Each dislocation segment was represented by a parametric space-curve of specified shape functions and associated degrees of freedom. Kinetic equations for the temporal evolution of the generalized coordinates were derived for a general 3-dimensional climbing and gliding motion of curved dislocation loops. It was shown that the evolution equations for the position, tangent and normal vectors at segment nodes were enough to describe any general 3-dimensional dislocation motion. When crystal-structure constraints were applied, just 2 degrees of freedom per node were adequate for constrained glide motion. The possible applications included adaptive node generation on interacting segments, variable time-step determination for the integration of the equations of motion, dislocation generation via the Frank-Read mechanism in face-centered cubic, body-centered cubic and diamond cubic crystals, loop-loop deformation and interaction and the formation of dislocation junctions.

Parametric Dislocation Dynamics - a Thermodynamics-Based Approach to Investigations of Mesoscopic Plastic Deformation. N.M.Ghoniem, S.H.Tong, L.Z.Sun: Physical Review B, 2000, 61[2], 913-27