Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions

Abstract

Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled energy whose minimizers are free from uncontrollable errors on the atomistic/continuum interface. In this paper a consistent coupling in three dimensions is proposed. The main achievement of this work is to identify and efficiently treat a modified Cauchy-Born continuum model which can be coupled to the exact atomistic model. The convergence and stability of the method is confirmed with numerical tests.

29 pages, 1 Matlab code. Typos corrected, exposition improved

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Cited by in corpus (15)

• Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions
• Theory-based Benchmarking of the Blended Force-Based Quasicontinuum Method
• Energy-Based Atomistic-to-Continuum Coupling Without Ghost Forces
• Analysis of Boundary Conditions for Crystal Defect Atomistic Simulations
• A posteriori error control for a quasicontinuum approximation of a periodic chain
• Construction and sharp consistency estimates for atomistic/continuum coupling methods with general interfaces: a 2D model problem
• A quasinonlocal coupling method for nonlocal and local diffusion models
• A Posteriori Error Estimation and Adaptive Algorithm for the Atomistic/Continuum Coupling in 2D
• On atomistic-to-continuum couplings without ghost forces in three dimensions
• Blended Ghost Force Correction Method for 3D Crystalline Defects
• Analysis of the Residual Type and the Recovery Type a Posteriori Error Estimators for a Consistent Atomistic-to-Continuum Coupling Method in 1D
• Formulation and optimization of the energy-based blended quasicontinuum method
• An atomistic/continuum coupling method using enriched bases
• A priori and a posteriori $W^{1,\infty }$ error analysis of a QC method for complex lattices
• Accuracy of computation of crystalline defects at finite temperature