Mechanical models and numerical simulations in nanomechanics: A review across the scales

Abstract

This work gives an overview of the theoretical background and of the numerical modelling framework used to describe the mechanical properties and the response of materials on scales ranging from the atomistic, through the microstructure and all the way up to the macroscale. In order to describe the dual nature of the structure of matter, which is continuous when viewed at large length scales and discrete when viewed at the atomic scale, plus the interdependence of these scales, multiscale modelling is required to complement the continuum and the atomistic models. More specifically, what we aim for in this review is to present and discuss the following basic conceptual models, as well as the methodologies that accompany them: (a) discrete models such as ab initio, atomistic / molecular, mesoscopic; (b) continuum mechanics models (CMM) comprising pure CMM, non-local elasticity CMM, higher-order strain gradient and higher-order nonlocal strain gradient elasticity CMM, and surface elasticity CMM; (c) multiscale material models (MMM). Since the field of nanomechanics is currently a rapidly expanding research area, the presented state-of-the art is by no means exhaustive. It simply outlines the research efforts that go behind formulating numerical models for the solution of problems in nanomechanics. Despite the advantages that boundary element methods (BEM) have in solving problems at the physical scale, either as stand-alone or in combination with finite element methods (FEM), their application to multiscale modelling is still limited, despite the promise they seem to hold.