|dc.description.abstract||In the first part of this dissertation, we develop a long-time moving window framework using Molecular Dynamics (MD) to model shock wave propagation through a one-dimensional monatomic chain. The moving window formulation follows the propagating shock front allowing us to model shock wave propagation much longer than conventional non-equilibrium MD (NEMD) simulations. This formulation also significantly decreases the required domain size and thus reduces the overall computational expense. The domain is divided into a purely atomistic window region containing the shock front flanked by boundary regions on either end which incorporate continuum shock conditions. Spurious wave reflections are removed by employing a damping band method using the Langevin thermostat applied locally to the particles in each boundary region. The moving window effect is achieved by adding/removing atoms to/from the window and boundary regions, and thus the shock wave front is focused at the center of the window region indefinitely. We simulate the shock through a one-dimensional monatomic chain using either the Lennard-Jones, modified Morse, or Embedded Atom Model (EAM) interatomic potential. We first perform verification studies to ensure proper implementation of the thermostat, potential functions, and damping band method, respectively. Next, we track the propagating shock and compare the actual shock velocity and average particle velocity to their corresponding analytical input values. From these comparisons, we optimize the linear shock Hugoniot relation for the given ``lattice" orientation and compare these results to those in literature. When incorporated into the linear shock equation, these new Hugoniot parameters are shown to produce a stationary wave front. Finally, we perform one-dimensional moving window simulations of an unsteady, structured shock up to a few nanoseconds and characterize the increase in the shock front's width.
While atomistic methods have successfully modeled different aspects of shock wave propagation in materials over the past several decades, they nevertheless suffer from limitations which restrict the total runtime and system size. Multiscale methods have been able to increase the length and time scales that can be modeled but employing such schemes to simulate wave propagation and evolution through engineering-scale domains is an active area of research. In the next part of this dissertation, we develop two distinct moving window approaches within a Concurrent Atomistic-Continuum (CAC) framework to model shock wave propagation through a one-dimensional monatomic chain. In the first method, the entire CAC system travels with the shock in a conveyor fashion and maintains the shock front in the middle of the overall domain. In the second method, the atomistic region follows the shock by the simultaneous coarsening and refinement of the continuum regions. The CAC and moving window frameworks are verified through dispersion relation studies and phonon wave packet tests. We achieve good agreement between the simulated shock velocities and the values obtained from theory with the conveyor technique, while the coarsen-refine technique allows us to follow the propagating wave front through a large-scale domain. This work showcases the ability of the CAC method to accurately simulate propagating shocks and also demonstrates how a moving window technique can be used in a multiscale framework to study highly nonlinear, transient phenomena.
The one-dimensional CAC shock wave studies demonstrate how coupled atomistic-continuum methods can describe large domains and model dynamic material behavior for a much lower computational cost than traditional atomistic techniques. However, these multiscale frameworks suffer from wave reflections at the atomistic-continuum interfaces due to the numerical discrepancy between the fine-scaled and coarse-scaled models. Such reflections are non-physical and may lead to unfavorable outcomes such as artificial heating in the atomistic region. In the third part of this dissertation, we develop a technique to allow the full spectrum of phonons to be incorporated into the coarse-scaled regions of a periodic concurrent atomistic-continuum (CAC) framework. This scheme tracks phonons generated at various time steps and thus allows multiple high-frequency wave packets to travel between the atomistic and continuum regions. Simulations performed with this method demonstrate the ability of the technique to preserve the coherency of waves with a range of wavevectors as they propagate through the domain. This work has applications for systems with defined boundary conditions and may be extended to more complex problems involving waves randomly nucleated from an impact within a multiscale framework.
While the one-dimensional CAC moving window framework produced some very noteworthy results, the physical applications of this framework are limited because a 1D domain cannot support dislocations or transverse atomic motion. Thus, in the fourth part of this dissertation, we develop a two-dimensional CAC formulation to model shock wave propagation through a single-crystal lattice for long simulation times. To achieve this, we develop sophisticated algorithms for the boundary conditions, neighbor lists, governing equation, and parallelization scheme. Additionally, since shearing effects can modify atomic behavior in a two-dimensional system, we also implement Gaussian integration in order to obtain more accurate forces. We incorporate moving window methods to track an elastic shock for several nanoseconds, and such methods require advanced numerical techniques to dynamically coarsen/refine atomic planes. We compare our simulation results to analytical models as well as previous atomistic and CAC data and discuss the apparent effects of lattice orientation on the shock response of two FCC crystals. We then use the moving window techniques to perform parametric studies which analyze the shock front's structure. Finally, we compare the efficiency of our model to MD simulations. This two-dimensional work showcases the framework's capability for simulating dynamic shock evolution over long runtimes and opens the door to more complex studies involving shock propagation through composites and alloys.
In the Conclusion of this dissertation, we provide a summary of the aforementioned research endeavors and review their contributions to the broader scientific community. Additionally, we discuss our current work which involves modeling the behavior of medium entropy alloys using a large-scale, three-dimensional CAC framework.||en_US