Page 233 - Mechanics of Asphalt Microstructure and Micromechanics

Models for Asphalt Concrete 225

Damage
The strain is assumed to be a function of both stress and damage (D, same definition
as 7-42).
dε C σ n
= 1
dt 1 ( − D) m
dD C σ v
= 2
dt 1 ( − D) μ
(7-59)
Where C 1 , C 2 , n, m, m are material constants depending on temperature.
Collop et al. (2006) extended the above formulas into 3D cases and developed nu-
merical implementations. The simplicity of the model structure is advantageous.

7.8 3D Constitutive Model for Asphalt Pavements
Oeser and Moller (2004) developed a generalized 3D viscoplastic constitutive model for
AC. Its 1-D presentation is as follows:

Strain Components
σ
ε (, , ) = ε σ, ) + ε (, , ) + ε (, ,, ) + ε ( , ) (7-60)
σ
σ
(
T
T
T
t
T
t
T
t
t
ges el ve vp th
·
In which s is stress; T is temperature; and e ges (t, s, T) is overall strain rate, depen-
dent on s, T;
The Elastic Component
σ
εσ T) = (7-61)
(,
el E (,
σ T)
H
The Viscoelastic Component
σ − E (, ε t, σ T)
σ T)⋅
,
(
ε t(, σ T) = k ve (7-62)
,
ve ησ T)
(,
K
This actually indicates that the elastic component and the viscoelastic component
are in parallel.
The Viscoplastic Component
σ
ε (, σ T) = (7-63)
t
,
vp ησ T(, )
N
This actually indicates that the viscoplastic component is in series with the visco-
elastic part.
The Thermal Component
ε tT) = T α ⋅ (7-64)
(,
th T
The material parameters E 11 , E k , h K , h N are dependent on both temperature and stress.
The intergranular tensile stress s H develops as a result of the lateral strain of the
inhomogeneous material.