Page 322 - Mechanics of Asphalt Microstructure and Micromechanics

314 Ch a p t e r N i n e

In summary, DEM applications in AC include those using idealized microstructure
(Collop et al., 2004, 2007, 2006); those that incorporated 2D micrsotructure (Buttlar and
You, 2001; You and Buttlar, 2004, 2006); and those using a user-defined irregular particle
model (Liu and You, 2008). In terms of contact models, the non-linear film-thickness-
dependent contact model (Collop et al., 2006) deserves special attention. It was well
recognized (Cheung and Cebon, 2007) that the stiffness of asphalt binder changes with
the film thickness. This feature should be included for future DEM applications.

9.6 Equivalent Ellipsoid Approach
For irregular particles, the translational motion equation is the same as Equation 9-1.
However, the rotational motion equations are quite different and can be written as in
Equation 9-31.
∑ M = I dω x − ( I − ) − I ( dω y −ωω ) − I (ω − ω 2 ) I ( d ω z + ωω ) (9-31a)
I ωω
−
2
(
x
x
dt y z y z xy dt z x yz y z zx dt x y
∑ M = I dω y − ( I − I ωω − I ( dω z −ωω ) − I (ω − ω 2 ) I ( d ω x + ωω ) (9-31b)
−
2
(
)
y
y
dt z x x z yz dt x y zx z x xy dt z y
∑ M = I dω z − ( I − I ωω − I ( dω x −ωω ) − I (ω − ω 2 ) I ( d ω y + ωω ) (9-31c)
−
2
)
(
z
z
dt x y x y zx dt y z xy x y yz dt z x
Where M x , M y , M z are the external force momentums against x,y,z axes on the par-
ticle; w x , w y , w z are the rotational velocity of the particle; I x , I y , I z , I xy , I xz and I yz are the six
mass momentums. These equations follow the general format of dynamics of rigid bod-
ies (Hibbeler, 1974). Figure 9.22 presents real particles in contact. Compared to spheres
in contact, real contact is much more complicated; the particle mass momentums are
usually not isotropic. To completely abide by the irregular geometry of real particles is
a challenging job, as it requires a full development of contact-detecting algorithms. The
existing codes (Lin and Ng, 1997) prompt the possibilities or approximating irregular
particles with ellipsoids with equal mass and mass momentums. The major reason for
investigating the feasibility of this idea is the requirement of using a huge number of

a. Representation by Voxels b. Representation by Clump
3-D
FIGURE 9.22 Representations of particles of irregular shape by using clump in PFC .