The role of the patch test in 2D atomistic-to-continuum coupling methods
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.
Cite
@article{arxiv.1101.5256,
title = {The role of the patch test in 2D atomistic-to-continuum coupling methods},
author = {Christoph Ortner},
journal= {arXiv preprint arXiv:1101.5256},
year = {2011}
}
Comments
Version 2: correction of some minor mistakes, added discussion of multiple connected atomistic region, minor improvements of style