Development and Analysis of the Blended Energy-Based Quasicontinuum Method.

摘要

A major goal of materials science is to predict the macroscopic properties of materials from their microscopic structure. For this purpose, it is necessary to understand the behavior of defects in these materials. We propose a computational tool, the blended energy-based quasicontinuum method (BQCE) for the simulation of defects such as cracks, dislocations, vacancies, and interstitials in crystalline materials.;The BQCE method provides a cheaply computed approximation to a computationally expensive atomistic energy. We give a numerical analysis focused on the error of BQCE in approximating the minimizers of this atomistic energy. We also consider the error of BQCE in approximating lattice instabilities, which are associated with the motion and formation of defects. We use our numerical analysis to derive optimal choices of the approximation parameters involved in BQCE, and we perform a computational test to validate our analytic results.;As formulated in this thesis, the BQCE method applies only to materials with Bravais lattice structure. However, we propose novel continuum energies which we believe are ideally suited for use in extending BQCE to multi-lattices. Our models are similar to the classical Cauchy-Born energy, but achieve a higher order of accuracy. In addition their use in extending BQCE, these models may potentially be used for the direct simulation of technologically important materials such as graphene and silicon in the diamond lattice state.