Page 448 - Mechanics of Asphalt Microstructure and Micromechanics

440 C hapter T h ir te en

it to a temperature T = 300K. The heat up rate is ΔT = 25K every 25 steps. The tempera-
ture is fixed after the final temperature T = 300K is achieved. Then the temperature is
controlled in an NVT ensemble. It is also ensured that the energy remains constant after
the annealing procedure.
Depending on loading conditions, the mechanical forces can be applied with vari-
ous constraints. For example, the shear and tensile loading can be applied to the 3D
asphalt-quartz interface structure for investigating the stress-strain relationships. To
impose shear loading conditions, the solid bounding wall parallel to the asphalt-rock
interface is moving in tangential direction at a constant velocity. Uniaxial tension
boundary conditions involve the application of deformation at a constant strain rate
normal to the interface plane, while the lateral boundaries are prescribed as stress free
and thus allowed to contract during the deformation process.
The interfacial asphalt layer stress-strain relationship is analyzed by using statistical
mechanics with the stress and strain definitions presented in 13.2.5.3 and 13.2.5.4. The
interface width, statistics, and radial distribution function are measured as a function of
distance from the interface. The MD simulations allow state variables to be analyzed in
terms of dynamic properties including radial distribution function (RDF), mean squared
displacement (MSD), space-time correction function, structural properties (atomistic
configuration), and energetic properties (energy evolution, temperature profile).
Using the mechanisms presented in the previous section, Figures 13.11a and b pres-
ent the shear stress-strain curve and uniaxial tensile stress-strain curve for the interface
model. These simulations provide insight into the interface shear/tension strength of
the molecule and the critical strains for onset of different modes of deformation. Figure
13.12a depicts a snapshot as nano-pores occur. Figure 13.12b shows a viscosity-time
step relationship of asphalt-aggregate interface under shear loading. For more details of
these simulations and other studies, please refer to the three papers (Lu and Wang,
2008; Lu and Wang, 2009; Lu and Wang, 2010).
13.2.11 3M Continuum and Electromagnetic-Mechanical Coupling

13.2.11.1 3M Continuum
Stone-based materials are highly heterogeneous. Due to the significant difference in
stiffness of the component materials (for example, aggregates versus binder), aggre-
gate may be subjected to a significant degree of rigid (relatively) rotation. Due to the
close packing of the aggregate particles, the strain gradient is also important and
therefore the non-local-type continuum theory should be adopted. By considering the
electromagnetic-mechanical coupling, the 3M (Micromorphic, Microstretch, and Micro-
polar) micro-continuum, non-local, and coupled theory proposed by Eringen (1999)
may have advantages.

13.2.11.2 Multi-Physics Coupled Constitutive Relation
The effect of electromagnetic-mechanical coupling can be evaluated using reaxFF. In
molecular dynamics, particles have a point charge representation used to compute the
Coulomb interactions (this is generally presented as a static limit of Maxwell’s equa-
tions valid after all transients have decayed to zero). Yet, in the case of reaxFF, the
charges on each atom are distributed over the size of the atom so that Coulomb interac-
tions between atoms are shielded as the atoms come together, allowing electrostatic
interactions between bonded atoms (conventionally shielded in other force fields). The
energy of each atom depends on the net charge in such a way as to properly describe