A discrete–continuous model of three-dimensional dislocation elastodynamics

Abstract

Unraveling the deformation mechanism of materials under extremely high strain rate is critical from both scientific and engineering viewpoints. The elastodynamic effect of 3D high-speed dislocations is one of the fundamental problems, but still remains largely unknown. The challenges lie in the fully temporal–spatial coupling feature, the requirement of recording the dislocation motion history, and the treatment of temporal–spatial singularities. These make the related theoretical derivation and numerical methods be much more complicated than that based on the quasi-static framework. To overcome these difficulties, in the current work, we presented an efficient discrete–continuous model which couples the three-dimensional discrete dislocation elastodynamics (DDE) with the finite element method (FEM) in the elastodynamic framework. It successfully reproduced the fully-resolved elastodynamic field of non-uniformly moving dislocations, and demonstrated the capability of dealing with the subsonic and supersonic dislocation in a unified framework. The free surface effect can also be easily captured. Several intriguing features of high-speed dislocations are also disclosed. The current work leads to an exciting opportunity to understand the collective behavior of high-speed dislocations under complicated shock loading conditions in an efficient way.