An efficient implicit method for discrete dislocation dynamics 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.

arXiv comment19 pages, 8 figures

References in corpus (11)

• Intermittent dislocation flow in viscoplastic deformation
• Multi-scale modeling of dislocation-precipitate interactions in Fe: from molecular dynamics to discrete dislocations
• Machine learning plastic deformation of crystals
• Submicron plasticity: yield stress, dislocation avalanches, and velocity distribution
• Quenched pinning and collective dislocation dynamics
• Dislocations Jam At Any Density
• Determination of the universality class of crystal plasticity
• Dynamical correlations near dislocation jamming
• Criticality of relaxation in dislocation systems
• The Emergence and Role of Dipolar Dislocation Patterns in Discrete and Continuum Formulations of Plasticity
• Abnormal subgrain growth in a dislocation-based model of recovery

Cited by in corpus (4)

• Dislocation Avalanches: Earthquakes on the Micron Scale
• Accelerating discrete dislocation dynamics simulations with graph neural networks
• Dynamic Length Scale and Weakest Link Behavior in Crystal Plasticity
• Avalanche Dynamics and the Effect of Straining in Dislocation Systems with Quenched Disorder