The role of the patch test in 2D atomistic-to-continuum coupling methods∗

Christoph Ortner

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

  • Volume: 46, Issue: 6, page 1275-1319
  • ISSN: 0764-583X

Abstract

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For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction, (iii) volumetric scaling of the interface correction, and (iv) connectedness of the atomistic region. The extent to which these assumptions are necessary is discussed in detail.

How to cite

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Ortner, Christoph. "The role of the patch test in 2D atomistic-to-continuum coupling methods∗." ESAIM: Mathematical Modelling and Numerical Analysis 46.6 (2012): 1275-1319. <http://eudml.org/doc/276383>.

@article{Ortner2012,
abstract = {For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction, (iii) volumetric scaling of the interface correction, and (iv) connectedness of the atomistic region. The extent to which these assumptions are necessary is discussed in detail.},
author = {Ortner, Christoph},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Atomistic models; atomistic-to-continuum coupling; quasicontinuum method; coarse graining; ghost forces; patch test; consistency; atomistic models},
language = {eng},
month = {3},
number = {6},
pages = {1275-1319},
publisher = {EDP Sciences},
title = {The role of the patch test in 2D atomistic-to-continuum coupling methods∗},
url = {http://eudml.org/doc/276383},
volume = {46},
year = {2012},
}

TY - JOUR
AU - Ortner, Christoph
TI - The role of the patch test in 2D atomistic-to-continuum coupling methods∗
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2012/3//
PB - EDP Sciences
VL - 46
IS - 6
SP - 1275
EP - 1319
AB - For a general class of atomistic-to-continuum coupling methods, coupling multi-body interatomic potentials with a P1-finite element discretisation of Cauchy–Born nonlinear elasticity, this paper adresses the question whether patch test consistency (or, absence of ghost forces) implies a first-order error estimate. In two dimensions it is shown that this is indeed true under the following additional technical assumptions: (i) an energy consistency condition, (ii) locality of the interface correction, (iii) volumetric scaling of the interface correction, and (iv) connectedness of the atomistic region. The extent to which these assumptions are necessary is discussed in detail.
LA - eng
KW - Atomistic models; atomistic-to-continuum coupling; quasicontinuum method; coarse graining; ghost forces; patch test; consistency; atomistic models
UR - http://eudml.org/doc/276383
ER -

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