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.

Multiscale Analysis of Fracture of Carbon Nanotubes Embedded in Composites

“…Due to the enormous difference in scales involved in correlating the macroscopic properties with the microscopic physical mechanisms of nanostructured materials, multiscale analysis is necessary (see, e.g., Shenoy et al, 1999;Curtin and Miller, 2003;Ghoniem et al, 2003). We adopt here a multiscale mechanics method to study the deformation and fracture behaviors of CNT-reinforced composites.…”

Multiscale Materials Modeling of Structural Materials for Next Generation Nuclear Reactors

“…Computational studies of dislocation activity can be performed at several different length and time scales. In some cases, a multi-scale modeling approach is adopted (Ghoniem et al 2003). Core properties and atomic mechanisms are simulated using first principles calculations and molecular dynamics simulations.…”

“…Dislocation motion is thought to be the main mechanism for deformation, because a fairly high density of network dislocations are generated during irradiation, and the dislocation sink strength for point defects is much higher that the grain boundary sink strength for point defects. Computational studies of dislocation activity can be performed at several different length and time scales (Ghoniem, Busso et al 2003) that are shown in Fig. 1.…”

Multiscale Finite Element Modeling of the Coupled Nonlinear Dynamics of Magnetostrictive Composite Thin Film

“…In recent time, multiscale modeling and computation have become powerful tool in solving many problems related to strongly coupled dynamics and multiphysics phenomena in material science and engineering [1,2]. Such an attempt, with judicious choice of the mathematical models which represent the mutually inseparable physical processes at the molecular scale, the lattice scale, the microstructural scale, and at the continuum scale, can be highly reliable in interpreting the experimental results and also in designing new materials and devices with desired multifunctionality.…”