Page 450 - Mechanics of Asphalt Microstructure and Micromechanics

442 C hapter T h ir te en

a. Nano-Pore Initiation under Tensile Loading
Shear Viscosity VS Timestep
1.60E+11
1.40E+11
1.20E+11
1.00E+11
Viscosity 8.00E+10

6.00E+10
Shear viscosity
4.00E+10
2.00E+10
0.00E+00
0 20 40 60 80 100 120
Timesteps(X100)
b. Viscosity at Interface under Shear Loading
FIGURE 13.12 Nano pore initiation and viscosity modeling based on MD simulations.

T
E
Where the tensor S ijkl , d ijkl , and ∈ ij are respectively the compliance at E = 0 and the
piezoelectric strain coefficient and unclamped dielectric coefficient; E is an external
electric field.
A linearly non-homogeneous magnetoelectroelastic properties formulation, which
coupled magnetic potential, electric potential, and continuum mechanics field (Lee and
Li, 2008) is also listed here:
⎛ ∇ ww ⎞ ⎛ 0⎞
2
⎜ y , ⎟ ⎛1 β ⎞ ⎜ ⎟
+ y
⎜ ∇ φ φ y , ⎟ ⎜ ⎟ = 0 (13-10)
2
0
⎜ ⎟
⎜ ⎟ ⎝ β ⎠ ⎜ ⎟
⎜ ⎝ ∇ ϕ ϕ ⎟ ⎠ ⎝ 0⎠
2
y ,