Nasr Ghoniem
Mechanical and Aerospace Engineering Department,
University of California at Los Angeles
Mechanics of Materials at the Nano and Micro Scales
An overview of theoretical and computational methods in the rapidly advancing field of Nanomechanics
and Micromechanics of materials is given. This overview emphasizes the Multiscale Modelling
of Materials (MMM) approach, which relies on a reduction of the degrees of freedom at
natural length scales. Two main challenges are identied in the MMM approach: (i) the computational
complexity of fully-coupled simulations, and (ii) inherent dificulties in describing the
temporal evolution of nano and microsystems with vastly dierent time-scales. We first introduce
the fundamental methods of quantum mechanics for description of the electronic degrees of freedom. Essential concepts are first introduced, followed by a presentation of the Local Density Approximation
(LDA) and Density Function Theory (DFT), pointing out to both limitations and successful
applications. Connections between "ab intio" methods and approximate interatomic potentials used
in Molecular Dynamics (MD) simulations are discussed. Atomistic simulation methods ( e.g. MD,
Langevin Dynamics (LD) and the Kinetic Monte Carlo (KMC)) and their applications at the nanoscale
are then discussed. When the length scale is too large for direct atomistic simulations and
too small to allow homogenization by continuum methods, reduction of the degrees of freedom is
accomplished by simulations of defect interactions, thus eliminating all electronic and atomic degrees
of freedom in this meso-scale. The role played by Dislocation Dynamics (DD) and Statistical
Mechanics (SM) methods in understanding microstructure self-organization, heterogeneous plastic
deformation, material instabilities and failure phenomena is also presented. Applications of the
methods presented here are given for a number of nano and micro material systems.
