Page 229 - Mechanics of Asphalt Microstructure and Micromechanics

Models for Asphalt Concrete 221

7.5 Viscoplastic Model with Microstructural Characteristics
Masad et al. (2005, 2007) and Tashman et al. (2005) developed a viscoplasticity model
for AC at relatively high temperatures. The unique features of this model include the
incorporation of microstructure and the particle orientation information measured from
2D and 3D images. The general principle follows the Perzyna model. For relatively high
temperatures, the viscoelastic component was considered as negligible and only the
viscoplastic component is considered.
ε = ε + ε vp (7-38)
ve
Total
They adopted a non-associated flow rule:
g ∂
ε vp = Γ ⋅ φ f () ⋅ (7-39)
ij ∂ σ
ij
Where e ij is the viscoplastic strain rate tensor; Γ is the fluidity parameter, which
· vp
–
establishes the relative rate of viscoplastic straining; g is the viscoplastic potential
–
function; f is the viscoplastic yield function; and <> are the Macauley brackets to ensure
–
·
the non-positive f( f ) leads to e vp = 0. These follow the same format as that by
Perzyna (1966).
Yield Function
Assuming a power law function for the yield surface, the yield function in the above
equation becomes:
⎧ 0 φ() < 0
f
φ() = ⎨ N (7-40)
f
f
f
⎩ ⎪ φ() = f φ() > 0
Where N is a constant to be determined experimentally.
Hardening
The hardening parameter is defined as:
⎡ ⎤
H C
κ = κ + ⎢1 − exp( − C + s ε ) )⎥ ⎥ (7-41)
(
0 C ⎢ r ε vp ⎥
C + s ⎣ vp ⎦
r ε
vp
H is an isotropic hardening coefficient; C r is a dynamic recovery coefficient; C s is a
· –
static recovery coefficient; and e vp is the effective viscoplastic strain rate. κ 0 defines the
–
initial yield surface and e vp is the effective viscoplastic strain.
Damage
A
ξ = v
S
σ
σ = where 0 ≤≤ 1 (7-42)
ξ
e − ξ
1