Page 173 - Mechanics of Asphalt Microstructure and Micromechanics

CHAPTER6

Fundamentals of

Phenomenological Models

he fundamental concepts of elasticity, viscosity, plasticity, viscoelasticity, and vis-
coplasticity are mathematical descriptions of the experimentally observed results
Ton stress-strain or stress-strain rate relationships. There are research efforts and
results on more fundamental mechanisms of the macroscopic deformation mechanism
behind these phenomenological models; however, they are beyond the scope of this
chapter. Continuum damage mechanics and fracture mechanics are a little different.
They involve some physical models regarding micro-cracking and macro-cracking.
Nevertheless, if possible, a concise description of the mechanism at lower scales (lower
than the macroscopic scale) will be presented. The guiding philosophy for this chapter
is to present minimum backgrounds of these topics so readers can be prepared for read-
ing more complicated topics and understanding Chapter 7 on the typical models used
in asphalt concrete.
Figure 6.1 presents a typical one-dimensional (1D) stress-strain relationship for a
metal specimen in tension (well defined behavior). The proportional limit, elasticity
limit (or yield stress), the hardening, the peak strength, and the residual or fracture
strength are the thresholds where different mechanics theories can be utilized or more
accurately utilized as different mechanisms control the deformation or strength charac-
teristics in these zones.
Within the proportional limit (Zone I), the material can be considered linear elastic.
The corresponding model may include linear elasticity. Between the proportional limit
and the yield stress, irrecoverable strain will be produced or Zone II, non-linear elastic-
ity such as hyperelasticity, may be a valid model. For most models, Zone I and Zone II
are often modeled as either linear elasticity or non-linear elasticity for simplicity. Once
the yield stress is reached, plastic deformation will be produced. The yield stress may
increase due to strain hardening or work hardening. The small zone of perfect plasticity
(where the yield stress is constant) might be very small and is often neglected. This zone
(Zone III) is often modeled as plasticity. For plasticity, the components may include the
initial yield stress or yielding criteria for complicated stress states; the hardening rule to
describe how the magnitude and center of the yield surface increase or move with plas-
tic strains or plastic work; the flow rule regarding the direction of the plastic deforma-
tion; and finally the peak strength or the ultimate yield surface. From the peak strength

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