Multiscale mechanical analysis of silicon nanostructures by combined finite temperature models
Z. Tang and N. R. Aluru
Computational Methods in Applied Mechanics and Engineering, 197, 3215-3224 (2008).

ABSTRACT
A multiscale model based on finite element method is proposed for mechanical
analysis of silicon nanostructures at finite temperature. By using a criterion
based on the Helmholtz free energy, appropriate lattice dynamics models are
seamlessly combined to compute mechanical properties. At each Computational
point, if the Helmholtz free energy calculated from the local quasiharmonic
model (LQHM) is close enough to that computed from the quasiharmonic model in
the reciprocal space (QHMK), the LQHM model is used to calculate the mechanical
properties, otherwise, the QHMK model is used. By using a silicon nanostructure
as an example, it is shown that the combined QHMK/LQHM multiscale model
significantly reduces the computational cost but maintains the accuracy of the
full QHMK model. Molecular dynamics results are also used for validation of the
combined multiscale model.