A line-free method of monopoles for 3D dislocation dynamics
We develop an approximation scheme for three-dimensional dislocation dynamics in which the dislocation line density is concentrated at points, or monopoles. Every monopole carries a Burgers vector and an element of line. The monopoles move according to mobility kinetics driven by elastic and applied forces. The divergence constraint, expressing the requirement that the monopoles approximate a boundary, is enforced weakly. The fundamental difference with traditional approximation schemes based on segments is that in the present approach an explicit linear connectivity, or 'sequence', between the monopoles need not be defined. Instead, the monopoles move as an unstructured point set subject to the weak divergence constraint. In this sense, the new paradigm is 'line-free', i. e., it sidesteps the need to track dislocation lines. This attribute offers significant computational advantages in terms of simplicity, robustness and efficiency, as demonstrated by means of selected numerical examples.
© 2018 Published by Elsevier Ltd. Received 18 June 2018, Accepted 3 September 2018, Available online 22 September 2018. AD and MO are grateful for support from the Stanback STEM program in Aerospace at Caltech. MPA is grateful for support from the Ministerio de Economa y Competitividad of Spain under grant number DPI2015-66534-R.
Accepted Version - 1806.04512.pdf