A Computational and Theoretical Investigation of the Accuracy of Quasicontinuum Methods

DOI10.1007/978-3-642-22061-6_3zbMath1245.74102arXiv1012.6031OpenAlexW1544636804MaRDI QIDQ2902567

Brian van Koten, Christoph Ortner, Xingjie Helen Li, Mitchell Luskin

Publication date: 21 August 2012

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1012.6031

Mathematics Subject Classification ID

Related Items (8)

Linear Stationary Iterative Methods for the Force-Based Quasicontinuum Approximation ⋮ Analysis of an energy-based atomistic/continuum approximation of a vacancy in the 2D triangular lattice ⋮ Generalized quasicontinuum modeling of metallic lattices with geometrical and material nonlinearity and variability ⋮ Upscaling of screw dislocations with increasing tangential strain ⋮ Finite element analysis of Cauchy-Born approximations to atomistic models ⋮ Formulation and optimization of the energy-based blended quasicontinuum method ⋮ Lattice Green function methods for atomistic/continuum coupling: theory and data-sparse implementation ⋮ Dynamics for Systems of Screw Dislocations

Cites Work

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• A field theoretical approach to the quasi-continuum method
• Multiscale plasticity modeling: Coupled atomistics and discrete dislocation mechanics
• Accuracy of quasicontinuum approximations near instabilities
• Iterative solution of the quasicontinuum equilibrium equations with continuation
• Iterative methods for the force-based quasicontinuum approximation: analysis of a 1D model problem
• Cauchy-Born rule and the stability of crystalline solids: Static problems
• Stability, instability, and error of the force-based quasicontinuum approximation
• Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method
• From molecular models to continuum mechanics
• Validity and failure of the Cauchy-Born hypothesis in a two-dimensional mass-spring lattice
• An adaptive finite element approach to atomic-scale mechanics. -- The quasicontinuum method
• Sharp Stability Estimates for the Force-Based Quasicontinuum Approximation of Homogeneous Tensile Deformation
• A generalized quasinonlocal atomistic-to-continuum coupling method with finite-range interaction
• A Quadrature-Rule Type Approximation to the Quasi-Continuum Method
• An Optimal Order Error Analysis of the One-Dimensional Quasicontinuum Approximation
• An Analysis of Node-Based Cluster Summation Rules in the Quasicontinuum Method
• On Atomistic-to-Continuum Coupling by Blending
• An analysis of the effect of ghost force oscillation on quasicontinuum error
• Analysis of a One-Dimensional Nonlocal Quasi-Continuum Method
• Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model
• Analysis of a quasicontinuum method in one dimension
• Analysis of a force-based quasicontinuum approximation
• Convergence Analysis of a Quasi‐Continuum Approximation for a Two‐Dimensional Material Without Defects
• Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics

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