A Computational and Theoretical Investigation of the Accuracy of\n Quasicontinuum Methods

2010/12/29 by Brian Van Koten, Van Koten, Brian, Xingjie Helen Li +5 · 2 citations
Engineering · Materials Science · #Advanced Numerical Analysis Techniques #Composite Material Mechanics #Elasticity and Material Modeling #FOS: Mathematics #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Microstructure and mechanical properties #Numerical Analysis (math.NA)

paper · pdf · doi:10.48550/arxiv.1012.6031

openalex publication_date 2010/12/29 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

We give computational results to study the accuracy of several quasicontinuum\nmethods for two benchmark problems - the stability of a Lomer dislocation pair\nunder shear and the stability of a lattice to plastic slip under tensile\nloading. We find that our theoretical analysis of the accuracy near\ninstabilities for one-dimensional model problems can successfully explain most\nof the computational results for these multi-dimensional benchmark problems.\nHowever, we also observe some clear discrepancies, which suggest the need for\nadditional theoretical analysis and benchmark problems to more thoroughly\nunderstand the accuracy of quasicontinuum methods.\n

Citations

• Iterative Methods for the Force-based Quasicontinuum Approximation
• A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D
• Analysis of Energy-Based Blended Quasicontinuum Approximations
• Numerical optimization

Cited by

• Linear Stationary Iterative Methods for the Force-based Quasicontinuum\n Approximation
• A priori and a posteriori W^1,\∞ error analysis of a QC method\n for complex lattices

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