2011/01/27 by Christoph Ortner, Ortner, Christoph · 2 citations
Materials Science · Engineering · #Microstructure and mechanical properties #Nanopore and Nanochannel Transport Studies #Block Copolymer Self-Assembly
paper · pdf · doi:10.48550/arxiv.1101.5256
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.