Modeling dislocations and heat conduction in crystalline materials: atomistic/continuum coupling approaches

Abstract

Dislocations and heat conduction are essential components that influence properties and performance of crystalline materials, yet the modelling of which remains challenging partly due to their multiscale nature that necessitates simultaneously resolving the short-range dislocation core, the long-range dislocation elastic field, and the transport of heat carriers such as phonons with a wide range of characteristic length scale. In this context, multiscale materials modelling based on atomistic/continuum coupling has attracted increased attention within the materials science community. In this paper, we review key characteristics of five representative atomistic/continuum coupling approaches, including the atomistic-to-continuum method, the bridging domain method, the concurrent atomistic-continuum method, the coupled atomistic/discrete-dislocation method, and the quasicontinuum method, as well as their applications to dislocations, heat conduction, and dislocation/phonon interactions in crystalline materials. Through problem-centric comparisons, we shed light on the advantages and limitations of each method, as well as the path towards enabling them to effectively model various material problems in engineering from nano-to mesoscale.

Moving window techniques to model shock wave propagation using the concurrent atomistic-continuum method

“…One of the primary challenges with concurrent multiscale methods is ensuring compatibility at the interface of the fine-scaled and coarse-scaled regions so as to mitigate spurious wave reflections and ghost forces [39]. Such non-physical phenomena arise for the following reasons: (i) a difference in governing equations exists between the atomistic and continuum regions, (ii) the spectrum of the coarse-scaled model has a much smaller cutoff frequency than that of the fine-scaled model causing the A-C interface to appear rigid to incoming high-frequency waves, and (iii) the interface region cannot support thermal vibrations of atoms.…”

“…Concurrent schemes such as these have had many achievements in modeling multiscale phenomena. Nevertheless, many of them involve a difference in material description across the interface, and most of them do not allow dislocation/phonon interactions or waves to travel into the continuum region [39].…”

One-dimensional moving window atomistic framework to model long-time shock wave propagation

“…The atomistic region is typically the region of interest where information from lower length scales is needed. In developing concurrent multiscale methods, it is imperative to ensure the compatibility of the interface region between fine-scaled and coarse-scaled regions [15]. One of the primary issues with concurrent atomistic/continuum methods is the phenomenon of spurious wave reflections at the interface.…”

A comparison of different continuum approaches in modeling mixed-type dislocations in Al

“…To date descriptions of dislocation cores have been best provided by atomic-scale simulations, which find that key characteristics of mixed-type dislocations cannot simply be extrapolated from those of pure-type ones [3][4][5][6][7][8][9]. Moreover, atomistic simulations are limited to nano/submicron length scale even with dedicated high-performance computing resources [10]. Thus, to understand plastic deformation of bulk materials, continuum modeling of dislocation core structures is desirable [11].…”