The role of the patch test in 2D atomistic-to-continuum coupling methods∗
Mathematics Institute, Zeeman Building, University of Warwick, CV4 7 AL Coventry, UK
Received: 14 March 2011
Revised: 21 October 2011
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.
Mathematics Subject Classification: 65N12 / 65N15 / 70C20
Key words: Atomistic models / atomistic-to-continuum coupling / quasicontinuum method / coarse graining / ghost forces / patch test / consistency
© EDP Sciences, SMAI, 2012