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

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

2011-01-27

arxiv.org/abs/1101.5256v2

Mathematics

Numerical Analysis

Version 2: correction of some minor mistakes, added discussion of multiple connected atomistic region, minor improvements of s

Scientific paper

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.

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