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Multiscale Modeling and Moisture Damage 433

is determined by how realistic the potential is. The degree of the complexity of an inter-
atomic potential also determines the amount of time needed for the simulation. Over
the years, a vast number of potentials have been developed that include pair potentials
(Haile, 1992), embedded-atom potentials (Farkas and Duranduru 2001), and bond-or-
der potentials (Dauber-Osguthorpe et al., 1988).
Potential energy functions are constructed as a function of atomic coordinates, mak-
ing use of parameters for describing bond stretching and bond-bending and allowing
for interactions between non-bonded atoms. Functional forms of potential energy func-
tions are shown in Figure 13.4. Generally, force-field methods describe the potential
energy of molecules as a sum of bond stretching (V str ), bond-angle bending (V bend ), out-
of-plane bending (V oop ), internal rotation (torsion) about bonds (V tors ), interactions be-
tween these motions (V cross ), van der Waals attractions and repulsions between non-
bonded atoms (V vdW ), and electrostatic interactions between non-bonded atoms (V el ):
V = V + V + V + V + V + V + V (13-2)
str bend oop tors cross vdW el
There are several excellent textbooks on MD simulations: Haile (1992), Leach (2001),
and Rapaport (2004).

13.2.5.3 Virial Strain
The atomistic quantities (trajectory quantities) must be averaged in space and time in
order to be compared with continuum concepts. Thus, the virial needs to be averaged
over space and time to converge to the Cauchy stress tensor.
The strain field is a measure of geometric deformation of the atomic lattice. The local
atomic strain is calculated by comparing the local deviation of the lattice from a reference
configuration. Usually, the reference configuration is taken to be the undeformed lattice.

FIGURE 13.4 Potential V
energy functions. Bonds
l l
l 0
q V
Angles
q 0 q
V
Improper w
Dihedrals w
w 0
V
Torsions
j j
V
Electrostatics r

V
van der Walls r