Multiscale modelling of nanomechanics and micromechanics: an overview

Abstract

Recent advances in analytical and computational modelling frameworks to describe the mechanics of materials on scales ranging from the atomistic, through the microstructure or transitional, and up to the continuum are reviewed. It is shown that multiscale modelling of materials approaches relies on a systematic reduction in the degrees of freedom on the natural length scales that can be identified in the material. Connections between such scales are currently achieved either by a parametrization or by a ‘zoom-out’ or ‘coarse-graining’ procedure. Issues related to the links between the atomistic scale, nanoscale, microscale and macroscale are discussed, and the parameters required for the information to be transferred between one scale and an upper scale are identified. It is also shown that seamless coupling between length scales has not yet been achieved as a result of two main challenges: firstly, the computational complexity of seamlessly coupled simulations via the coarse-graining approach and, secondly, the inherent difficulty in dealing with system evolution stemming from time scaling, which does not permit coarse graining over temporal events. Starting from the Born–Oppenheimer adiabatic approximation, the problem of solving quantum mechanics equations of motion is first reviewed, with successful applications in the mechanics of nanosystems. Atomic simulation methods (e.g. molecular dynamics, Langevin dynamics and the kinetic Monte Carlo method) and their applications at the nanoscale are then discussed. The role played by dislocation dynamics and statistical mechanics methods in understanding microstructure self-organization, heterogeneous plastic deformation, material instabilities and failure phenomena is also discussed. Finally, we review the main continuum-mechanics-based framework used today to describe the nonlinear deformation behaviour of materials at the local (e.g. single phase or grain level) and macroscopic (e.g. polycrystal) scales. Emphasis is placed on recent progress made in crystal plasticity, strain gradient plasticity and homogenization techniques to link deformation phenomena simultaneously occurring at different scales in the material microstructure with its macroscopic behaviour. In view of this wide range of descriptions of material phenomena involved, the main theoretical and computational difficulties and challenges are critically assessed.