Page 443 - Mechanics of Asphalt Microstructure and Micromechanics

Multiscale Modeling and Moisture Damage 435

• Hydrogen-bonds
• Weak or dispersive van der Waals (vdW) interactions.

In general, the elastic properties of materials can be expressed as the partial deriva-
tive of the free energy density with respect to the strain tensor that characterizes the
deformation.
−
=
GUTS (13-6)
Where G, U, T, and S represent free energy, internal energy, absolute temperature,
and entropy, respectively.
One can define the free energy density as:

Φ= G (13-7)
V
In the simplest 1D situation, the (scalar) stress is then is given by:
∂Φ
σ = (13-8)
ε ∂
The stress and strain can be related by Hooke’s law, s = Ee. The above relationships
can be conveniently extended to 3D formulations.
One can use the Energetic Elasticity Theory to link molecular or atomistic proper-
ties with overall elastic modulus. Energetic elasticity is characterized by the stretching
of atomic, metallic, covalent, or ionic bonds that leads to a change in potential energy in
the material.

13.2.6 Digital Specimen and Digital Test for Meso-scale Simulations
Clearly, at the meso-scale the digital specimen and digital test techniques can be used
for either upscaling or downscaling. A gradual homogenization approach at such scale
has been developed by Lutif et al. (2008). No further detailed discussions will be offered
for this section.

13.2.7 Multiscale Structure Characterization
Modeling without characterization is not complete. Characterization of the 3D multi-
scale structure using nano CT and micro CT is very important. Traditional nano devices
such as Atomic Force Microscope (AFM) and Scanning Electron Microscope (SEM) can
only characterize surface structure. A recent grant by NSF allows Virginia Tech to pur-
chase a Nano CT at 50-nanameter resolution. This is a very important step. The Vir-
ginia Tech Institute for Critical Technology and Applied Science (ICTAS) has various
micro CTs, the nano CT and the nano indentation system. They enable the characteriza-
tion of AC structure at various scales and mechanical properties at various scales for
modeling.

13.2.7.1 Interface Characterization
In previous chapters, microstructure characterization at mesoscale (0.1-millimeter resolu-
tion) has been discussed and the major technology presented is XCT. For features smaller
than this scale, micro CT at very high resolutions (0.5 μm) and nano CT is necessary.