Page 194 - Mechanics of Asphalt Microstructure and Micromechanics

186 Ch a p t e r S i x

FIGURE 6.10 Illustration of σ
the Kelvin model.

σ σ
1 2

η
R

σ

For constant stress (creep effect, s˙ = 0), the following solution can be obtained:
σ
ε = 0 1 ( − e −Rt/ η ) (6-100)
R
It should be noted that the Kelvin model cannot describe the relaxation phenome-
non.
6.3.6.3 Burgers Model
The Burgers model can be graphically expressed as in Figure 6.11.
The governing equations include:
ε = ε + ε + ε (6-101)
1 2 3
σ
ε =
1
R
1
σ
ε =
2 η
1
R σ
ε + 2 ε =
3 η 3 η (6-102)
2 2
The above equations lead to the following governing equation:
η η η ηη ηη
σ + ( 1 + 1 + 2 ) σ + 12 σ = η ε + 12 ε (6-103)
R R R R R 1 R
1 2 2 1 2 2 2
At constant stress, the above equation leads to the following solution (creep effect):
σ σ σ
ε() = 0 + 0 t + 0 ( − e − Rt 2 / η 2 ) (6-104)
1
t
R η R
1 1 2