Page 463 - Mechanics of Asphalt Microstructure and Micromechanics

Multiscale Modeling and Moisture Damage 455

damage. The simulations results indicate that the quartz surface is more susceptible to
moisture than Calcite. This is in agreement with macroscale experimental observations.
The major reason is that quartz is an acid substrate, whereas calcite has an alkaline incli-
nation which increases its affinity to asphalt and makes it less susceptible to water.

13.4 A Two-Scale Homogenization Method
Computational simulation based on 3D microstructure is very time expensive. Lutif et
al. (2009) proposed a multiscale approach in which a separate scale computation is per-
formed for each of the smaller structural scales. If statistical homogeneity at any small-
er length scale has been satisfied, a homogenization principle may be adopted to pro-
duce the field equations for the next larger length scale. In addition, damage can also be
modeled at each length scale by incorporating appropriate types of fracture mechanics
models to the analysis.
In this multiscale model, a global scale computation is performed concurrently with
the local scale analyses. Figure 13.18 illustrates a schematic depiction of a two-scale
problem. The global scale is considered to be statistically homogeneous, whereas the
local scale is heterogeneous. Note that the local scale size needs to meet the required
dimensions of the representative volume element (RVE), because the heterogeneous
mixture RVE is homogenized to produce its effective properties that are sequentially
updated to the global scale constitutive relations. In the local scale object, various sourc-
es of heterogeneity can be considered, such as particles, voids, and cracks. Cracks in the
local scale are modeled by implementing the cohesive zones, which are fictitious zones
embedded in the local scale body to represent the initiation and the propagation of
physical cracks.
The method developed by Lutif et al. (2009) and Souza (2008), which is based on the
finite element method, can be summarized in the following steps.
1. Input data for global and local scales.
2. Solve the global scale problem.
3. Apply global scale solution to the local scale problem.
4. Obtain local scale solution from the local scale RVE.
5. Homogenize local scale field variables.
6. Update homogenized local scale results to the global scale problem.

FIGURE 13.18 A schematic depiction of a global-local multiscale problem (Courtesy Y. R. Kim).