Page 436 - Mechanics of Asphalt Microstructure and Micromechanics

428 C hapter T h ir te en

valid. The only difference would involve the interfaces among the different micro-
continuums.
When the governing constitutive equation contains few variables, a hierarchical
coupling method is desired that can provide a more viable solution to concurrent cou-
pling techniques. In contrast, the concurrent coupling methods are preferred when the
constitutive relationship depends on more variables, so it is difficult to extract it by pre-
computing. From a numerical viewpoint, however, the two strategies are closely related
in that for both hierarchical and concurrent coupling methods, the key issue is to design
simulations at the micro-scale level that offer the needed macroscopic data. The two
strategies can be combined to yield optimal efficiency. For example, a concurrent simu-
lation can be used to pre-evaluate the constitutive equation for the hierarchical cou-
pling method.
Recent years have seen a surge of interest in developing concurrent multiscale mod-
eling methods that can obtain the same results as atomistic modeling at a lower compu-
tational price. The efficiency is accomplished by atomistically modeling selected small
sub-domains of the problem, while analyzing the rest of the domain using continuum
modeling. Table 13.1 summarizes the current multiscale modeling methods available in
open literature.

13.2.3 General Philosophy of Multiscale Modeling of AC
Figure 13.2 presents the general philosophy to resolve the multiscale modeling problem
for AC. AC typically consists of aggregates (including mineral fillers), asphalt binder,
interfacial transition zones, and voids. These components can be considered as micro-
continuums. Each of the micro-continuums and the interfaces can be modeled using the
Reaction Force Theory (van Duin et al., 2003; Goddard et al., 2006; and Chenoweth et al.,
2008) based on quantum mechanics, molecular dynamics, and thermal mechanics (sta-
tistical mechanics, and can be upscaled to continuum). Through the use of FEM and
with the consideration of the microstructure and the techniques of homogenization, the
material can be modeled as either a traditional continuum or 3M (micro-morphic, micro-
stretch, and micro-polar, Eringen, 1999) continuum. A macro-constitutive model for the
material can then be developed, represented by the upscaling process. The material
structure can be represented as digital specimens, which may represent the scales in
separate databases. For the downscaling process, solving a boundary value problem
would involve the use of the continuum model for the completely homogenized con-
tinuum, triggering the micro-continuum and directly MD and RFF calculations concur-
rently for zones of special interest. Numerically, the above problem can be resolved
concurrently or hierarchically.

13.2.4 Reaction Force Field Theory
In molecular mechanics/molecular dynamics, a force field refers to the functional form
and parameter sets used to describe the potential energy of a system of atoms. Force-
field functions and parameter sets are derived from both experimental work and high-
level quantum mechanical calculations.
The consistent-valence force field (CVFF) is a generalized valence force field. Pa-
rameters are provided for amino acids, water, and a variety of other functional groups.
The augmented CVFF was developed for materials science applications. It includes ad-
ditional atom types for aluminosilicates and aluminophosphates.