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

Abstract

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