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Hybrid atomistic -continuum modeling of inhomogeneous materials

Hong Zhou, University of Nebraska - Lincoln

Abstract

A robust and efficient method for hybrid atomistic-continuum modeling and simulation of material systems with isolated heterogeneities has been developed. In this method, the material in vicinity of a strong heterogeneity such as crack, grain boundary or dislocation is modeled accurately with fully-atomistic (FA) description while the vast material away from the heterogeneity is modeled efficiently with a quasicontinuum-based coarse-graining technique similar to the finite-element method. The hybrid description yields a reduced system consisting of the atoms of the FA regions and the pseudoatoms (element nodes) of the coarse-grained (CG) regions. Atomic free energy is used to determine the energetics of the material system at a given temperature and hence the nonlinear effects as well as the discrete nature of the near-heterogeneity material are captured. Monte-Carlo simulations are used to obtain the thermodynamic properties of the system. The use of finite-element-like coarse-graining technique enables modeling and simulation of material systems that are currently too large for application of fully atomistic simulation. ^ Two critical issues, which afflict all previous hybrid schemes spanning multiple length scales, are the presence of "ghost force" and gross underestimate of thermal motions due to coarse-graining. Various approaches aimed at addressing these two issues have been examined in detail. The studies have led to the development of an all-local treatment and a self-consistent-field technique, which reduce significantly the ghost force effects within the CG regions and near the CG-FA interface. Free-energy correction utilizing local harmonic approximation has been worked out to account for the thermal motions of the underlying atoms in the CG region that are assumed to move in concert with the element nodes. Stringent benchmark tests show that the self-consistent-field, hybrid atomistic-coarse-grained (SCF-HACG) method yields results in good agreement with those of more accurate, fully atomistic simulation over a wide range of thermodynamic states. ^ Finally, the SCF-HACG method has been applied successfully to simulate the grain boundary in Lennard-Jones bicrystal and the nanoindentation of silicon crystal. Each involves a material system with a strong heterogeneity. The results show that the combination of atomistic description in vicinity of the heterogeneity and the ability to simulate a physically large inhomogeneous system can provide not only accurate thermomechanical modeling near the heterogeneity but also accurate account for the influence of surrounding material(s) on the local behavior. This represents a significant progress in realistic modeling of multiscale phenomena. ^

Subject Area

Engineering, Materials Science

Recommended Citation

Zhou, Hong, "Hybrid atomistic -continuum modeling of inhomogeneous materials" (2006). ETD collection for University of Nebraska - Lincoln. AAI3225793.
http://digitalcommons.unl.edu/dissertations/AAI3225793

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