Consistent formulation for the Discrete-Continuous Model: improving complex Dislocation Dynamics simulations

A new and efficient formulation of the Discrete-Continuous Model (DCM) for the simulation of 3D dislocation dynamics in complex finite or periodic volumes is presented. As in previous versions, the improved model is based on a coupling between a Dislocation Dynamics (DD) code and a Finite Element (FE) code through eigenstrain theory. Short-range interactions are now handled more properly. Specifically, in the continuous limit the stress field driving the dislocation dynamics is now reconstructed consistently. Furthermore, the DCM can now handle nonstructured meshes, and free surface and interface handling does not depend on having a structured mesh anymore. Also numerical experiments shed some light on the influence of the choice of the FE quadrature. Some approximations are proposed and justified, and the use of advanced algorithmic techniques are used for time integration and the homogeneisation procedure to reach a high computational efficiency. Basic tests demonstrate the validity and the efficiency of the proposed strategy. Remarkably, it is demonstrated that for a periodic domain the DCM with a very fine FE mesh is actually faster than a corresponding classical DD simulation.