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.
Mots-clés : atomistic models, atomistic-to-continuum coupling, quasicontinuum method, coarse graining, ghost forces, patch test, consistency
@article{M2AN_2012__46_6_1275_0,
author = {Ortner, Christoph},
title = {The role of the patch test in {2D} atomistic-to-continuum coupling methods},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
pages = {1275--1319},
publisher = {EDP-Sciences},
volume = {46},
number = {6},
year = {2012},
doi = {10.1051/m2an/2012005},
mrnumber = {2996328},
zbl = {1269.82063},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an/2012005/}
}
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 PY - 2012 SP - 1275 EP - 1319 VL - 46 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an/2012005/ DO - 10.1051/m2an/2012005 LA - en ID - M2AN_2012__46_6_1275_0 ER -
%0 Journal Article %A Ortner, Christoph %T The role of the patch test in 2D atomistic-to-continuum coupling methods %J ESAIM: Mathematical Modelling and Numerical Analysis %D 2012 %P 1275-1319 %V 46 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an/2012005/ %R 10.1051/m2an/2012005 %G en %F M2AN_2012__46_6_1275_0
Ortner, Christoph. The role of the patch test in 2D atomistic-to-continuum coupling methods. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 46 (2012) no. 6, pp. 1275-1319. doi : 10.1051/m2an/2012005. http://www.numdam.org/articles/10.1051/m2an/2012005/
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