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

Published online by Cambridge University Press:  27 March 2012

Christoph Ortner
Christoph Ortner*
Affiliation:
Mathematics Institute, Zeeman Building, University of Warwick, CV4 7AL Coventry, UK. c.ortner@warwick.ox.ac.uk
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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.

Keywords

Atomistic modelsatomistic-to-continuum couplingquasicontinuum methodcoarse grainingghost forcespatch testconsistency

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Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 46 , Issue 6 , November 2012 , pp. 1275 - 1319
Copyright
© EDP Sciences, SMAI, 2012

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