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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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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