A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods

Abstract

We give computational results to study the accuracy of several quasicontinuum methods for two benchmark problems - the stability of a Lomer dislocation pair under shear and the stability of a lattice to plastic slip under tensile loading. We find that our theoretical analysis of the accuracy near instabilities for one-dimensional model problems can successfully explain most of the computational results for these multi-dimensional benchmark problems. However, we also observe some clear discrepancies, which suggest the need for additional theoretical analysis and benchmark problems to more thoroughly understand the accuracy of quasicontinuum methods.

25 pages, 9 figures, improved exposition, fixed typos

References in corpus (7)

• Accuracy of Quasicontinuum Approximations Near Instabilities
• A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D
• Iterative Methods for the Force-based Quasicontinuum Approximation
• Sharp Stability Estimates for the Force-based Quasicontinuum Method
• An Analysis of the Quasi-Nonlocal Quasicontinuum Approximation of the Embedded Atom Model
• Analysis of Energy-Based Blended Quasicontinuum Approximations
• Analysis of the quasi-nonlocal approximation of linear and circular chains in the plane

Cited by in corpus (6)

• Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions
• Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice
• The role of the patch test in 2D atomistic-to-continuum coupling methods
• Analysis of Energy-Based Blended Quasicontinuum Approximations
• Linear Stationary Iterative Methods for the Force-based Quasicontinuum Approximation
• A priori and a posteriori $W^{1,\infty }$ error analysis of a QC method for complex lattices