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Multiscale Modeling and Moisture Damage 427

Type D: problems that exhibit self-similarity in scales, such as the critical phenome-
na in fractals, turbulent transport, and statistical physics.
Type A and Type B problems feature the characteristic of scale separation, while
Type D problems are characterized by the special feature of statistical self-similarity.
The featured characteristics of each category generally guide the design of an efficient
multiscale modeling approach to be used.
13.2.2.5 Hierarchical vs. Concurrent Modeling
One traditional multiscale modeling approach is the hierarchical coupling method (se-
quential or serial coupling method) in which an effective macroscale model is deter-
mined in pre-processing steps using microscale models. The macroscale model is usu-
ally targeted for applications. Hierarchical coupling methods are well known to pass
parameters in sequence, i.e. from a lower hierarchy (smaller spatial or temporal scale)
to an upper one (larger spatial or temporal scale) and vice versa. The scheme of hierar-
chical multiscale modeling is illustrated in Figure 13.1 (Ghoniem and Cho, 2002). The
focus of multiscale modeling in current times, however, is more on the concurrent cou-
pling methods (Abraham et al., 1998). The concurrent coupling methods entail the link-
age of the macroscale and the microscale models in a domain based on a spatial decom-
position of the system into regions dominated by different length scales. Both the mac-
roscale and the microscale models are executed in each computation step (such as one
time step). This is how the terminology concurrent comes into being.
For asphalt mixtures, one additional complexity is their meso-scale heterogeneity,
the air-void, binder, and aggregate constituents. If these constituents are treated as
micro-continuums, for each micro-continuum, the above scale classification may be

FIGURE 13.1 Schematic illustration of a typical hierarchical multiscale modeling
(Ghoniem and Cho, 2002).