A continuum‐to‐atomistic bridging domain method for composite lattices

Abstract

AbstractThe bridging domain method is an overlapping domain decomposition approach for coupling finite element continuum models and molecular mechanics models. In this method, the total energy is decomposed into atomistic and continuum parts by complementary weight functions applied to each part of the energy in the coupling domain. To enforce compatibility, the motions of the coupled atoms are constrained by the continuum displacement field using Lagrange multipliers. For composite lattices, this approach is suboptimal because the internal modes of the lattice are suppressed by the homogeneous continuum displacement field in the coupling region. To overcome this difficulty, we present a relaxed bridging domain method. In this method, the atom set is divided into primary and secondary atoms; the relative motions between them are often called the internal modes. Only the primary atoms are constrained in the coupling region, which succeed in allowing these internal modes to fully relax. Several one‐ and two‐dimensional examples are presented, which demonstrate improved accuracy over the standard bridging domain method. Copyright © 2009 John Wiley & Sons, Ltd.