Page 204 - Mechanics of Asphalt Microstructure and Micromechanics

196 Ch a p t e r S i x

6.4.2.2 The Elastic/Viscoplastic Model
ε = ε + ε vp
e
ij ij ij
The rate equation is:
ε = ε + ε vp
e
ij ij ij
Perzyna introduced the static yield function (initial yield function):
F(σε p ) = f (σε p )/κ − 1 (6-161)
,
,
ij kl ij kl
κ
κ = (W )
p
ε p kl
p ∫
W = σε ij p
d
ij
0
W p is the accumulative plastic work.
The static yield function is assumed to be regular and convex. The formulation for
the rate of the viscoplastic strain is similar to that for the plastic strain:
f ∂
F >
ε vp = γ < Φ() (6-162)
ij ∂ σ
ij
g and Φ (F) are a viscosity parameter of the material, and a function showing the
dynamic behavior of the material.
−
1 12 ν f ∂
ε = s + δ s + γ < Φ() (6-163)
F >
ij 2 μ ij E ij ∂ σ
ij
6.5 Continuum Damage Mechanics (Lemaitre, 1996)
6.5.1 General Concepts of Continuum Damage Mechanics
Elasticity is for material structures with no defects: bonds among atoms are perfect and
atom configurations follow regular patterns. Viscoelasticity is for material structure
with relatively weak bonds. Plasticity is for materials with dislocations. Continuum
damage mechanics is valid for materials when their bonds start to break, or start to
sustain damage. Damage for different materials may be demonstrated as breakage of
bonds of long chain molecules of polymers; debonding between fibers and matrix in
composite materials; microdecohensions between inclusions and matrix; pore coalesc-
ing in the interfacial transition zones in concrete. In general, damage mechanics may be
interpreted as a mechanics that take into consideration existing defects and damage,
but smooths the local damage effects with continuum mechanics by using one or a few
damage parameters. It is unlike micromechanics where the details of microstructure
change must be considered. The two concise books that are recommended are Lemaitre
(1996) and Voyiadjis and Kattan (1999).
In AC, damage may be demonstrated as pore initiation in the binder, micro-pore
coalescence in the binder, mastic, and aggregate-binder or filler-binder interfaces.
CDM is valid when the continuum types of governing equations are valid through the
concept of effective stresses. There are several types of damage phenomena including