Page 464 - Mechanics of Asphalt Microstructure and Micromechanics

456 C hapter T h ir te en

The above procedure is actually a two-way coupling method. The state of
deformation observed on the global structure is passed to the boundary of the local
scale RVE, and the solution obtained from the local scale is homogenized and returned
to the global scale problem for the next time step. The two-way coupling is essentially
necessary when the problem is for viscoelasticity and evolved microstructure. This type
of problem involves viscoelasticity and cracking and is typically time, history, and space
dependent. In the multiscale modeling process, the global scale can be discretized with
a homogeneous finite element mesh, which may dramatically reduce the time required
for computation. The local scale, considering mixture heterogeneity, may take more
complicated meshes. Furthermore, a local scale RVE is attached to each global scale
integration point of selected global scale finite elements.
It is important to note that the results from the local scale analysis are homogenized
and linked to the global scale problem. The concept of homogenization replacement (Al-
len and Searcy, 2006) of a heterogeneous medium with a macroscopically equivalent
homogeneous one is applicable whenever the heterogeneous medium satisfies statistical
homogeneity. Homogenization is central to the idea of multiscale simulation and is
typically created through averaging local fields within the heterogeneous medium.
Equation 13-32 represents such an average:
1 μ
−
t =
μ+1
C ijkl () μ ∫ C ( t τ) dV (13-32)
ijkl
V μ
V
μ
μ+1
Where C ijkl is the averaged global scale modulus, C is the local scale modulus; m
ijkl
denotes the local length scale, m + 1 indicates the next larger length scale, that is the
m
global scale, V denotes the volume of the local scale object.
It is also noteworthy that the local scale RVE could include cracking. Souza (2008)
included a nonlinear viscoelastic cohesive zone model to enable the modeling of local
scale viscoelastic fracture. The cohesive zone model can predict damage evolution in
the global scale. Hence, the model can capture the formation of micro-cracking and the
propagation in the heterogeneous local scale RVE and update the local scale fracture
process to the global scale damage-dependent performance.
13.5 Future Development
While it is hard to accurately predict and evaluate the behavior of AC due to the reasons
outlined in Chapter 1, multiscale modeling of asphalt behavior presents a promising
potential to realistically model its behavior more accurately.
Research and education in the mechanics of asphalt have gained momentum in re-
cent years due mainly to the need to understand and predict the mixture behavior for
building long-lasting AC pavements. Nevertheless, significant efforts are still needed in
validating, refining, and integrating various existing models. Special efforts should go
to the exploration of complicated coupling phenomena such as rutting (large plastic
deformation) induced fatigue and vice versa. Development of a generalized FEM code
for these specific applications is a task that will benefit all researchers, educators, and
practicing engineers.