TY - JOUR
T1 - Bridging Methods for Atomistic-to-Continuum Coupling and Their Implementation
JO - Communications in Computational Physics
VL - 4
SP - 831
EP - 876
PY - 2010
DA - 2010/07
SN - 7
DO - http://doi.org/10.4208/cicp.2009.09.053
UR - https://global-sci.org/intro/article_detail/cicp/7657.html
KW - 
AB - <p style="text-align: justify;">Several issues connected with bridging methods for atomistic-to-continuum
(AtC) coupling are examined. Different coupling approaches using various energy
blending models are studied as well as the influence that model parameters, blending
functions, and grids have on simulation results. We use the Lagrange multiplier
method for enforcing constraints on the atomistic and continuum displacements in
the bridge region. We also show that continuum models are not appropriate for dealing
with problems with singular loads, whereas AtC bridging methods yield correct
results, thus justifying the need for a multiscale method. We investigate models that
involve multiple-neighbor interactions in the atomistic region, particularly focusing on
a comparison of several approaches for dealing with Dirichlet boundary conditions.</p>