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Published May 2021 | metadata_only
Journal Article

A semi-discrete line-free method of monopoles for dislocation dynamics


We develop a semi-discrete particle method for Volterra dislocation currents in which the particles, or monopoles, represent an element of line and carry a Burgers vector. The monopoles move according to mobility kinetics driven by elastic and applied forces. The divergence constraint of Volterra dislocation currents is enforced weakly through mesh-free interpolation and an explicit linear connectivity, or 'sequence', between the monopoles need not be defined. In this sense, the method 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, especially as regards the tracking of complex dislocation patterns, including topological transitions. We illustrate the range and scope of the method, by means of an example of application concerned with the plastic hardening of nano-sized grains under monotonic loading.

Additional Information

© 2021 Published by Elsevier Ltd. Received 30 September 2020, Revised 14 January 2021, Accepted 21 January 2021, Available online 13 March 2021. This work has been partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via project 211504053 - SFB 1060 and project 390685813 - GZ 2047/1 - HCM, and the Ministerio de Ciencia, Innovación y Universidades of Spain under grant number RTI2018-094325-B-I00. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional details

August 22, 2023
August 22, 2023