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

ESAIM: Mathematical Modelling and Numerical Analysis (2012)

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

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topOrtner, 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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