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used to simulate phenomena where the elasticity solution does not change with
the defect size (outside of a predefined core region) and phenomena where,
instead, the elasticity solution evolves in the neighborhood of the defect. Simu-
lations of a dislocation core, or of kinks on a dislocation, are examples of the
first class of phenomena, while the investigation of crack propagation is an
example of the second class. Green's function boundary condition (GFBC)
methods are well suited for the investigation of the former class of processes,
while boundary condition methodologies that couple finite-element-continuum
domains to atomistic regions are designed for modeling the latter. This second
class of boundary condition methods is examined below. Several groups have
proposed GFBC methodologies,
137-141
and, in the following, as an example,
we will discuss the one suggested by Sinclair et al.
140
and then expanded by
Rao et al.
141
The simplest approach to simulate an infinite dislocation line is to
consider an atomistic cell of cylindrical shape, aligned along the dislocation
line itself, and embed it into a fixed continuum region [Figure 6(a)]. Such a
configuration is usually referred to as 2D because the thickness of the cell along
Figure 6
Simulation cells for studying dislocation cores in the 2D case. (a) In the fixed
boundary approach, region 1 is the atomistic region, where atoms are allowed to relax,
while region 3 is the fixed outer shell mimicking the continuum medium. (b) In the
GFBC method of Rao et al.,
141
an intermediate shell (region 2) is inserted between the
atomistic (region 1) and the continuum domains (region 3).
