Page 439 - Mechanics of Asphalt Microstructure and Micromechanics

Multiscale Modeling and Moisture Damage 431

To understand the chemical reactions, mechanical behavior, and electromechanical
coupling, an atomistic level of interaction and behavior is needed. This requires quan-
tum mechanics, which is numerically very challenging (i.e., on only a few hundred at-
oms). The Reaction Force Field (ReaxFF) Theory bridges the length scale between quan-
tum mechanics and molecular dynamics. The ReaxFF simulations (van Duin et al., 2003;
Goddard et al., 2006; and Chenoweth et al., 2008) provide a full-physics, full-chemistry
description of processes in materials, otherwise unreachable via quantum mechanics
(QM), and constitute the ideal tool for studying reactivity on surfaces and condensed
matter. The results of these simulations will provide an atomistic description of the pro-
cesses and structure, including kinetic conditions, that will provide key insight into op-
timizing asphalt mixtures, as well as provide complementary information to the avail-
able experimental methodologies and continuum-level simulation of these materials.

13.2.5 Molecular Dynamics (MD)

13.2.5.1 MD Fundamentals
Traditional MD will increase the computational efficiency at the cost of accuracy. Under
National Science Foundation (NSF) support for the Unified Approach for Multiscale
Characterization, Modeling, and Simulation of Stone-based Infrastructure Materials,
MD simulations of asphalt binder-aggregate interfaces have been developed (Lu and
Wang, 2008; Lu and Wang, 2009, 2010; Lu, 2010), where the binder model developed by
Zhang and Greenfield (2007a, 2007b and 2008). An atomistic FEM approach is being
developed to bridge the length scale between MD and continuum mechanics. This is a
hierarchal approach but may be more realistically achievable and provide better links
between state-of-the-art research and current practice using the continuum and phe-
nomenological models.
MD was originally used in thermodynamics and physical chemistry to calculate the
collective or average thermochemical properties of various materials including gases,
liquids, and solids. There are two basic assumptions made for the standard molecular
dynamics simulations (Haile, 1992):
1. Molecules or atoms are described as a system of interacting material points,
whose motions are described dynamically with vectors of instantaneous posi-
tions and velocities. The atomic interaction has a strong dependence on the
spatial orientations of atoms and the distances among them.
2. The simulated system is usually treated as an isolated domain with conserved
energy. Usually there is no mass change in the system. Equivalently, the num-
ber of atoms in the system remains the same. However, non-conservative tech-
niques are also available, which can model the dissipation of the kinetic energy
into the surrounding media.
As shown in Figure 13.3, the MD simulation can be represented as a loop using the
finite difference method. This method involves the solution of the classical equations of
motion for a system of N atoms. In classical statistical mechanics, the phase space tra-
jectories (position vectors and velocity vectors) {r i (t), v i (t)}, are calculated by integrating
Newton’s second law:
∂ ( , r )
Ur r ,...,
mr =− 1 2 N ≡ F , i = 12 , ,....,N (13-1)
¨
ii r ∂ i
i