Page 232 - Mechanics of Asphalt Microstructure and Micromechanics

224 Ch a p t e r Sev e n

The thermo-viscoplastic strain rate is written as:

eθ
e = e + Γ() F ) F ∂ +αθδ (7-53)
θφ(
ij ij F ∂σ T ij
0 ij
Where F is yield function; Γ(q ) is temperature dependent fluidity parameter; f is
the function that plays the role of a flow coefficient depending on the distance from the
present stress point to the yield surface F; and <> are the Macauley brackets.
The model did not include the damage effect and the microstructure effect. Through
the use of triaxial tests including isotropic compression, conventional triaxial compres-
sion, reduced triaxial extension, and creep tests at various temperatures, the model pa-
rameters are calibrated.

7.7 Stress-Dependent Elastoviscoplastic Constitutive Model
with Damage
Collop et al. (2003) developed an elastoviscoplastic model with damage considerations.
The following presents its 1-D formulations. The model followed the Perzyna decom-
position of the total strain into three components.
ε = ε + ε + ε (7-54)
Total el ve vp

The Elastic Component
ε t() = σ t()/ E (7-55)
el 0
Where s is the stress and E 0 is the modulus of elasticity of the elastic element.

The Viscoelastic Component
−
t dJ t t ) ′
(
ε t() = J ( ) σ t() + ∫ ve σ t() ′ ddt′ (7-56)
0
−
ve ve dt t ) ′
(
0
J ve is viscoelastic creep compliance
t is dummy integration variable
The Viscoplastic Component
−
t dJ ( t t ) ′
ε () = J ( ) σ t() + ∫ vp σ t() ′ ddt′ (7-57)
0
t
−
vp vp dt t ) ′
(
0
J vp is viscoplastic creep compliance
Stress Dependency
dε σ
= Kσ = Kσ n−1 σ = (7-58)
n
dt λ
m
Where K and n are materials constants. The stress dependency and non-linearity are
represented.