Consistent Energy-Based Atomistic/Continuum Coupling for Two-Body Potentials in One and Two Dimensions

Abstract

This paper addresses the problem of consistent energy-based coupling of atomistic and continuum models of materials, limited to zero-temperature statics of simple crystals. It has been widely recognized that the most practical coupled methods exhibit large errors on the atomistic/continuum interface (which are often attributed to spurious forces called "ghost forces"). There are only few existing works that propose a coupling which is sufficiently accurate near the interface under certain limitations. In this paper a novel coupling that is free from "ghost forces" is proposed for a two-body interaction potential under the assumptions of either (i) one spatial dimension, or (ii) two spatial dimensions and piecewise affine finite elements for describing the continuum deformation. The performance of the proposed coupling is demonstrated with numerical experiments. The coupling strategy is based on judiciously defining the contributions of the atomistic bonds to the discrete and the continuum potential energy. The same method in one dimension has been independently developed and analyzed in Li and Luskin (arXiv:1007.2336).

31 pages

References in corpus (6)

• Stability, Instability, and Error of the Force-based Quasicontinuum Approximation
• 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
• A Priori and A Posteriori Analysis of the Quasi-Nonlocal Quasicontinuum Method in 1D
• Iterative Methods for the Force-based Quasicontinuum Approximation
• Energy-based ghost force removing techniques for the quasicontinuum method

Cited by in corpus (21)

• Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions
• Theory-based Benchmarking of the Blended Force-Based Quasicontinuum Method
• Energy-Based Atomistic-to-Continuum Coupling Without Ghost Forces
• Analysis of an Energy-based Atomistic/Continuum Coupling Approximation of a Vacancy in the 2D Triangular Lattice
• Interpolants of Lattice Functions for the Analysis of Atomistic/Continuum Multiscale Methods
• A posteriori error control for a quasicontinuum approximation of a periodic chain
• A review of Local-to-Nonlocal coupling methods in nonlocal diffusion and nonlocal mechanics
• Continuum Surface Energy from a Lattice Model
• The role of the patch test in 2D atomistic-to-continuum coupling methods
• Analysis of Energy-Based Blended Quasicontinuum Approximations
• A quasinonlocal coupling method for nonlocal and local diffusion models
• A Posteriori Error Estimates for Energy-Based Quasicontinuum Approximations of a Periodic Chain
• Positive-Definiteness of the Blended Force-Based Quasicontinuum Method
• Linear Stationary Iterative Methods for the Force-based Quasicontinuum Approximation
• Blended Ghost Force Correction Method for 3D Crystalline Defects
• Quasinonlocal coupling of nonlocal diffusions
• Formulation and optimization of the energy-based blended quasicontinuum method
• A consistency study of coarse-grained dynamical chains through a nonlinear wave equation of mixed type
• Analysis of an optimization-based atomistic-to-continuum coupling method for point defects
• Analysis of a Sinclair-type domain decomposition solver for atomistic/continuum coupling
• On a Gamma-convergence analysis of a quasicontinuum method