On Determining Continuum Quantities of Non-Equilibrium Processes via Molecular Dynamics Simulations

摘要

In this dissertation, a high-fidelity atomistic-to-continuum link for highly non-equilibrium processes has been established by making several modifications to Hardy’s theory. Although Hardy’s thermomechanical quantities were derived analytically to conserve mass, momentum and energy, they have not been rigorously tested and validated numerically in the past.udHence the first task was to investigate the effectiveness of ensemble averaging in removing thermal fluctuations and compare with conventional time averaging for fcc crystals simulated using both equilibrium and non-equilibrium molecular dynamics (MD) simulations, where the non-equilibrium process was introduced by a shock impact. It has been found that the ensemble averaging has better convergence than time averaging due to the statistical independence of the thermomechanical quantities computed using ensemble averaging.udThe second task was to test the validity of Hardy’s theory by checking if it is able to conserve mass, momentum and energy numerically. A few highly non-equilibrium processes were simulated using MD, including Gaussian wave and shock impact propagation in 1D and 3D fcc crystals. Based on the test results, a new normalization rule has been proposed so that the computed thermomechanical quantities can conserve the fundamental properties more accurately. To a large extent, Hardy’s theory has been found to be valid regardless of the width of the localization function, the interatomic potential and crystal structure, and with and without ensemble averaging.udTo further test the validity of Hardy’s theory for more complex non-equilibrium processes, where plastic deformation is accomplished through dislocation glide and slip band emission, a crack propagation problem in iron crystal with a pre-created center crack is simulated using MD. The computed Hardy’s thermomechanical quantities can generally conserve mass, momentum and energy. Exceptions have been found around the crack region, where the computed quantities cannot obey the balance of energy but still conserve mass and momentum.udThe results from this dissertation will help 1) inspire confidence in employing Hardy’s theory with the proposed modifications to analyze MD simulation results, especially for non-equilibrium thermomechanical processes and 2) pave the way for concurrent atomistic/continuum coupled simulations.