Page 275 - Mechanics of Asphalt Microstructure and Micromechanics
P. 275
F inite Element Method and Boundar y Element Method 267
Viscoelasticity
ε = ε + ε i
e
σ V
V V
ε = ε e + ε p
σ EP
EP EP
Elastoplasticity
σ = σ + σ
T
EP V ε
a. Constitutive Model in Total Stress and Strain
Viscoelasticity
Δ σ V Δε = Δε + Δε V i
e
V
Δσ EP Δε = Δε EP + Δε EP
e
p
Elastoplasticity
Δσ = Δσ + Δσ Δε
T
EP V
b. Constitutive Model in Incremental Stress and Strain
(where V denotes viscoelasticity component, EP denotes elastoplasticity component)
FIGURE 8.5 The SHRP viscoplasticity model.
Thus,
C ijkl = C ijlk = C jikl = C klij (8-74)
The detailed derivation of the elasticity tensor was not presented.
The Viscous Component
. n
ε = ( − b n ) −1 ζ∂ W( ) (8-75)
ε
e
−1
i
1
e
ε
ρ
Equation (8-75) basically states that the current inelastic strain rate is proportional
to the current stress.
