Objective Molecular Dynamics: An atomistic analogue of exact solutions of continuum mechanics

Abstract

This thesis is aimed at the computational development and application of the method of Objective Molecular Dynamics (OMD). At first, the thesis develops OMD as an efficient computational tool by focusing on the development of the effective implementation of the method for the time-dependent translation group. Later, it focuses on its usage in studying gas and dislocation dynamics under strong non-equilibrium conditions. OMD is a generalization of periodic MD to non-equilibrium cases that exploits the invarianceof the equations of MD and the underlying potential energy hypersurface. The method is used to inform higher-scale theories. This is motivated by the fact that OMD enables forging of rigorous links between fundamental quantum mechanics and nonstandard macroscopic continuum mechanics. It provides an atomistic analogue of motions that are exact solutions of the macroscopic equations for general solids or fluids. The other advantage is that in OMD only a few atoms are actually simulated, but the full infinite set of atoms satisfy exactly the MD equations. This considerably reduces the computational cost of the problem. The thesis makes comparison of the predictions from the particle-level method of OMD with solutions of theNavier-Stokes (NS) equations combined with Newtonian and Fourier models for a compressible, heat- conducting monoatomic gas. By studying in detail the macroscopic motions corresponding to diverse OMD simulations, the breakdown of NS equations is investigated and a generalization of the Navier-Stokes equations based on Rivlin-Ericksen (RE) theory is postulated. RE theory agrees accurately with NS for slow flows but makes significant improvements over NS relation in capturing far-from-equilibrium momentum transport. This work finds application in facilitating the use of continuum CFD modeling even in the regime of far-from-equilibrium flows which will be highly useful for the modeling of vehicle scale hypersonic and micro-nano scale flows. Next, the method is applied to study high-temperature chemically reacting flows in various regimes relevant to hypersonic flows to provide in-depth molecular level analysis. The study explores dissociation, recombination, and energy exchange in nitrogen flows and reports the existence of non-equilibrium population distributions and significant microscopic selectivity of reactive processes. This is known to have a direct impact on continuum thermo-chemistry models. The comparison of OMD with CFD shows the inadequacy of the widely used standard Park's model in capturing the correct physics of strong thermo-chemical non-equilibrium gas. Finally, the same method is applied to investigate a very different system than the previous cases. It is demonstrated that OMD is a powerful method of simulation for dislocation motion, including cross-slip and the transition to twinning, as well as frictional sliding by careful choice of initial conditions. The study investigates the phenomenon of cross-slipping where screw dislocation leaves its habit plane and glides in a conjugate cross-slip plane. It is answered how large a stress can FCC nickel sustain before it cross-slips in non-equilibrium regime under the effect of a large strain rate at finite temperature by taking a kinetic viewpoint. Surprisingly, transition state theory captures some aspects of the behavior of cross-slip under high-rate deformation even in these far-from-equilibrium situations. This finding can assist the modeling of cross-slip at the mesoscopic scale within the framework of dislocation dynamics simulation under high-rate conditions. The thesis also reports some important pathways that material chooses to relax the stress under different macroscopic motions. Another contribution is to show how OMD techniques can be used to study homoenergetic dilatational flow exhibiting spontaneous condensation. Moreover, to illustrate that both solid boundaries and fluid can be treated in the same exact OMD simulation, the transitional flow of argon gas exhibiting slip in a nanochannel is also studied. The thesis also reports the modeling of sliding surfaces using the framework of OMD.