An efficient implicit method for discrete dislocation dynamics simulations

TL;DR

This paper introduces an implicit numerical scheme that dramatically accelerates discrete dislocation dynamics simulations, enabling larger and longer simulations without sacrificing accuracy, and is applicable to 3D modeling.

Contribution

The paper presents a novel implicit numerical method that improves the speed and efficiency of dislocation dynamics simulations, especially for stiff equations.

Findings

The method is several orders of magnitude faster than existing approaches.

It maintains accuracy without requiring dislocation annihilation.

The approach is adaptable to three-dimensional simulations.

Abstract

Plastic deformation of most crystalline materials is due to the motion of lattice dislocations. Therefore, the simulation of the interaction and dynamics of these defects has become state-of-the-art method to study work hardening, size effects, creep and many other mechanical properties of metallic specimens. Lot of efforts have been made to make the simulations realistic by including specific dislocation mechanisms and the effect of free surfaces. However, less attention has been devoted to the numerical scheme that is used to solve the equations of motion. In this paper we propose a scheme that speeds up simulations by several orders of magnitude. The scheme is implicit because this type is the most efficient one for solving stiff equations that arise due to the long-range nature of dislocation interactions. The numerical results show that the method is not only faster than other approaches at the same numerical precision, but it can also be efficiently applied even without dislocation annihilation. The suggested method significantly increases the achievable volume and/or duration of discrete dislocation dynamics simulations and can be generalized for 3D simulations as well.