Summary: Multiscale mechanical analysis of silicon nanostructures by
combined finite temperature models
Zhi Tang, N.R. Aluru *
Department of Mechanical Science and Engineering, Beckman Institute for Advanced Science and Technology,
University of Illinois at Urbana-Champaign, Urbana, IL 61801, United States
Received 1 September 2007; received in revised form 23 October 2007; accepted 21 November 2007
Available online 14 January 2008
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.
Ó 2007 Elsevier B.V. All rights reserved.
Keywords: Multiscale analysis; Silicon nanostructures; Local quasiharmonic; k-Space quasiharmonic; Quasicontinuum method; Finite temperature
In recent years, silicon nanostructures have attracted
great interest as building blocks for nanoelectromechanical