A hybrid model was suggested for the discrete analysis of self-forces and non-conservative effects in 3-dimensional dislocation dynamics. Dislocations were idealized as being line defects in an homogeneous linear elastic medium. Each dislocation line consisted of interconnected straight segments. The displacement and stress fields which were associated with the segment were formulated, for general anisotropy and arbitrary crystal symmetry, by using an integral formalism. The stress field of each dislocation was then computed via a linear superposition of the stress contributions from all of the segments. The dynamics were described by solving Newton’s equation of motion for each portion of a dislocation. The differential equations for the individual segments were coupled via the line tension. This was treated discretely by calculating the self-interaction force among segments which belonged to the same dislocation. Non-conservative motion was introduced by considering the osmotic force that arose from the emission of adsorbing point defects at the climbing segment. The effect of temperature was introduced by regarding the crystal as a canonical ensemble, and by including a stochastic Langevin force.

Introduction of a Hybrid Model for the Discrete 3D Simulation of Dislocation Dynamics. D.Raabe: Computational Materials Science, 1998, 11[1], 1-15