Chemistry Reference
In-Depth Information
FEAt Method
The
finite-element combined with atomistic modeling
(FEAt)
method,
82-86
developed by Kohlhoff et al. in 1988, is one of the oldest atomistic/
continuum coupling methods, and it was inspirational in the development of
several other coupling schemes (e.g., the one used in the CADD methodology
discussed below).
This method is based on three main ideas: first, to only use displacements
in the coupling procedure; second, to use a
mutual-displacement boundary
conditions
scheme; and third, to match the elastic constants in order to equili-
brate the stresses between the atomistic and the continuum domains. The
reason for the first assumption is that, because of the local nature of the con-
tinuum and the nonlocal nature of the atomistic regime, the stress principles
governing the two regions are significantly different, and they should not enter
the coupling procedure. In other words, the use of forces is explicitly avoided
in this scheme, so no direct interaction occurs between the stress fields of the
two media. We will now illustrate the mutual-displacement boundary condi-
tions scheme. As shown in Figure 2, the atomistic core region is connected to
the large continuum domain through a transition region (shaded area in the
figure) where the two representations overlap, i.e., in this area atoms and
nodes coincide. The transition region is subdivided into two zones: one
(labeled II in the figure) provides the boundary conditions for the continuum,
and the other (labeled III) provides the boundary conditions for the atomistic
region. More specifically, in zone II the displacements of the finite-element
nodes are determined by the displacements of the atoms with which they coin-
cide, while in zone III the nodal displacements dictate how the atoms in that
zone should move. This procedure ensures equality of the displacement fields
in the atomistic region and in the continuum.
Transition Region
III
I
IV
II
Atomistic Region
Continuum Region
Figure 2
Schematic representation of the FEAt coupling scheme. The atomistic region
(I) is embedded inside a continuum region (IV) and the two zones are coupled through
an extended interface zone (shaded area). The transition region is divided into two zones
(II and III), each providing boundary condition for either the continuum (zone II) or the
atomistic region (zone III).
