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).


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.