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

Abstract

a b s t r a c tSurface 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 thermodynamicallyconsistent 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.

Summation rules for a fully nonlocal energy-based quasicontinuum method

“…There is clearly room for improvement here but even this rather ad hoc choice performs orders of magnitude better than the other summation rules. A more detailed analysis of optimal values for the effective interaction radii in particular in the presence of free surfaces can be found in Amelang and Kochmann (2015).…”

“…In contrast, the new second-order rule assigns sampling atoms to the faces of tetrahedral elements, which automatically takes care of free surfaces by representing all surface-nearest lattice sites by those sampling atoms on the surface. We will report details of how surfaces and interfaces can be modeled by the new scheme in Amelang and Kochmann (2015); here, we will show that the second-order scheme can successfully master the combined challenges of free surfaces and microstructure formation.…”

Automatic adaptivity in the fully nonlocal quasicontinuum method for coarse‐grained atomistic simulations

“…Here, we briefly summarize the key theoretical concepts at the level required for subsequent discussions. The interested reader is referred to [15,16,32] for further details. As in atomistics, an ensemble of N atoms is described by their positions q = {q 1 , .…”

Multiresolution molecular mechanics: Surface effects in nanoscale materials

“…A wide range of existing approaches have been proposed to solve this issue. In general, existing models may be classified into three groups: (I) enhanced classical continuum mechanics [9,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38], (II) atomic-based continuum analysis [39][40][41][42][43] and (III) coarse-grained atomistic approaches [44][45][46][47][48].…”

“…This aforementioned drawback calls for a powerful multiscale model that may not depend on the continuum framework such as the constitutive stress-strain relationship but pure atomistic description, which motivated the development of coarse-grained atomistic models [45][46][47][48][53][54][55][56][57][58][59] in group III. The nonlocal quasicontinuum (QC) method [45-47, 53-56, 60] is a typical representative method and has been recently applied to study surface effect in nanoscale structures based on the newly proposed summation rules in [45]. Since the proposed summation rules employed in the quasicontinuum framework are specifically designed for linear interpolation shape functions, the consistent extension to high order interpolation shape functions is not clear, as has been clearly observed in [61,62].…”