Bridging domain methods for coupled atomistic–continuum models with <i>L</i>² or <i>H</i>¹ couplings

Abstract

Abstract A bridging domain method for coupled atomistic–continuum models is proposed that enables to compare various coupling terms. The approach does not require the finite element mesh to match the lattice spacing of the atomic model. It is based on an overlapping domain decomposition method that makes use of Lagrange multipliers and weight functions in the coupling zone in order to distribute the energy between the two competing models. Two couplings are investigated. The L 2 coupling enforces the continuity of displacements between the two models directly. The H 1 coupling involves the definition of a strain measure. For this purpose, a moving least‐square interpolant of the atomic displacement is defined. The choice of the weight functions is studied. Patch tests and a graphene sheet with a crack are studied. It is shown that both continuous and discontinuous weight functions can be used with the H 1 coupling whereas the L 2 coupling requires continuous weight functions. For the examples developed herein, the L 2 coupling produces less error in the zone of interest. The flexibility of the H 1 coupling with constant weight function may be beneficial but the results may be affected depending on the topology of the bridging zone. Copyright © 2008 John Wiley &amp; Sons, Ltd.