Surface effects in nanoscale structures investigated by a fully-nonlocal energy-based quasicontinuum method
J. S. Amelang and D. M. Kochmann
Mechanics of Materials, 90, 166-184 (2015).

ABSTRACT
Surface effects in nanoscale mechanical systems such as nanoporous solids or
small-scale structures can have a significant impact on the effective material
response which deviates from the material behavior of bulk solids. Understanding
such phenomena requires modeling techniques that locally retain atomistic
information while transitioning to the relevant macroscopic length scales. We
recently introduced a fully-nonlocal energy based quasicontinuum (QC) method
equipped with new summation rules. This technique accurately bridges across
scales from atomistics to the continuum through a thermodynamically-consistent
coarse-graining scheme. Beyond minimizing energy approximation errors and
spurious force artifacts, the new method also qualifies to describe free
surfaces, which is reported here. Surfaces present a major challenge to
coarse-grained atomistics, which has oftentimes been circumvented by costly ad
hoc extensions of the traditional QC method. We show that our new
coarse-graining scheme successfully and automatically reduces spurious force
artifacts near free surfaces. After discussing the computational model, we
demonstrate its benefits in the presence of free surfaces by several
nanomechanical examples including surface energy calculations, elastic size
effects in nano-rods and in plates with nano-sized holes. Overall, we
demonstrate the importance of surface effects as well as a new strategy to
accurately capture those computationally via coarse-grained atomistics.