Surface effects in nanoscale structures investigated by a fully-nonlocal energy-based quasicontinuum method

• The fully-nonlocal QC method with optimal summation rules captures nanoscale surface effects.
• Model adaptivity efficiently reduces full atomistic resolution to where it is required.
• We demonstrate elastic size effects in nanoscale single-crystals.
• We report size effects in plastically-deforming nanoscale metallic sheets.

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.