Page 385 - Mechanics of Asphalt Microstructure and Micromechanics

Simulation of Asphalt Compaction 377

et al., 1996) has proven to be quite accurate in predicting the permanent deformations
of AC. This model has also been used by Scarpas and many others. Zhang and Wang
(2007) used this model to represent the mastic properties and successfully applied it to
model the static compression of AC. Model predictions and experimental observations
agree very well. Zhang and Wang's work falls into the theme topic of digital specimen
and digital test techniques where the microstructure of asphalt concrete is considered.
Another model is the porous viscoplasticity model. This viscoplasticity model
takes the void content as an internal variable and has been successfully used by Wang
et al., (2007) to model the field compaction process. This model is described here in
more detail.
The model is based on the theory proposed by Gurson (1977) and modified by Tver-
gaard (1981). Rather than assuming plastic incompressibility, the porous plastic model
considers hydrostatic components of stresses and strains. It takes the effect of void nu-
cleation and growth into account. It shows the importance of plastic dilatation. Guler et
al. (2002) used this Gurson-Tvergaard model in compaction simulation trying to cali-
brate the material parameters using experimental results.
The material model includes the following components:

• Linear elasticity:
ε = C el σ (11-7)
el
ij ijkl kl
• Yield function dependent on confining stress:
⎛ ⎞ ⎛ ⎞
=
F = ⎜ q ⎟ + 2 qf cosh ⎜ − q 3 p ⎟ −( 1 + qf ) = 0 (11-8)
2
⎝ σ y ⎠ 1 ⎝ 2 2 σ y ⎠ 3

• Associated plastic flow:
·
pl ·
ε = λ F ∂ (11-9)
ij ∂ σ
ij
• Isotropic strain hardening:
σ = ( )
σ ε
pl
y y m (11-10)
The evolution of the equivalent plastic strain:
1− ( ) f σε pl · = σ ε pl · (11-11)
ym ij ij

The evolution of the volume fraction f:
· pl · ·
f = (1 − f )ε + Aε pl (11-12)
ii m
Rate dependent yielding can be modeled in ABAQUS and the failure can be mod-
eled in ABAQUS explicit. Temperature-dependent material parameters can be defined
as a tabular function of temperature.