Page 433 - Mechanics of Asphalt Microstructure and Micromechanics

Multiscale Modeling and Moisture Damage 425

All materials are composed of atoms. Existing defects such as cracks can lead to
stress concentrations under loads, which in turn lead to nucleation of dislocations or
generation of new material surfaces due to strong deformation at highly localized re-
gions such as the crack tips. These nano- and microscale defects typically include point
defects, dislocations, interfaces, and grain boundaries that essentially determine the
mechanical properties of materials and structures. According to the statistical law of
large numbers (LLN), continuum analyses are valid only for large enough systems that
include a substantial number of defects at the meso or above-meso scales. Continuum
approaches cease to work as the system size approaches the average separation dis-
tance in-between defects.
13.2.2.2 Atomistic Modeling
The capability of continuum modeling of construction materials and structures is fur-
ther limited by a number of factors. First, a wide variety of experimental observations
on the mechanical behavior of materials cannot be explained satisfactorily within the
paradigm of continuum mechanics. These observations include the dislocation patterns
in fatigue and creep of metals, surface roughening and crack nucleation in fatigue of
concretes, and some common problems in generic building materials such as the statis-
tical nature of brittle failure, the inherent inhomogeneity of plastic deformation and
plastic flow localization in shear bands, and the effects of size, geometry, and stress
state on the yield properties. Second, constitutive equations in continuum models are
usually phenomenological descriptions that are determined within a certain range of
temperature, stress state, strain rate, and material conditions. Without a clear physico-
chemical understanding, the behavior of materials under unanticipated conditions be-
yond the measured range becomes unknown, which in turn significantly limits the
widespread use of experimentally-derived constitutive equations. Third, nowadays,
transportation engineering has evolved to emphasize small length-scale phenomena,
such as to develop high performance materials based on nanotechnologies. Equally
imperative is the fact that the technology of micro-electro-mechanical systems (MEMS)
has become mature for monitoring the reliability of structures, which points to the need
for a more physically-based approach than continuum modeling.
Being faced with the challenges to the continuum modeling of construction materi-
als, together with the recent advancement of computation technologies that enable
large-scale computing, the development of more efficient numerical methods for mod-
eling complex physical phenomena in materials has become imperative and attractive.
The availability of large-scale computing capability has, in the past decade, greatly pro-
pelled the modeling of material phenomena into a more rational direction: the atomistic
modeling and simulation, mainly quantum molecular dynamics (QMD) and classic
molecular dynamics (MD), in which individual nucleons, electrons, and atoms are ex-
plicitly followed during their dynamic evolution. Opposite to the continuum-based
analysis that attempts to reduce the complexity of a material system’s behavior by a
process of reduction of its degree of freedom (DOF), researchers now are trying to rep-
resent large numbers of DOFs and solve for them numerically. The last decade has seen
tremendous advances on a number of computational and physical fronts in atomistic
simulation techniques, with rigorous ways to approximate the quantum mechanical
behavior of atoms and molecules. These advances in QMD have been parallel to the
development of physically-based inter-atomic potentials for performing more accurate
classical MD simulations. It is noteworthy that the quantum simulation methods are
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much more time expensive (10 to 10 times more) than classical atomistic simulations.