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The role of the patch test in 2D atomistic-to-continuum coupling methods
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Ortner, Christoph. (2012) The role of the patch test in 2D atomistic-to-continuum coupling methods. ESAIM: Mathematical Modelling and Numerical Analysis, Vol.46 (No.6). pp. 1275-1319. ISSN 0764-583X
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Official URL: http://dx.doi.org/10.1051/m2an/2012005
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.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QA Mathematics |
| Divisions: | Faculty of Science > Mathematics |
| Journal or Publication Title: | ESAIM: Mathematical Modelling and Numerical Analysis |
| Publisher: | EDP Sciences |
| ISSN: | 0764-583X |
| Date: | 2012 |
| Volume: | Vol.46 |
| Number: | No.6 |
| Number of Pages: | 45 |
| Page Range: | pp. 1275-1319 |
| Identification Number: | 10.1051/m2an/2012005 |
| Status: | Peer Reviewed |
| Publication Status: | Published |
| Access rights to Published version: | Restricted or Subscription Access |
| URI: | http://wrap.warwick.ac.uk/id/eprint/48597 |
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