Abstract
Among the efficient numerical methods based on atomistic models, the quasi-continuum (QC) method has attracted growing interest in recent years. The QC method was first developed for crystalline materials with Bravais lattice and was later extended to multilattices [Tadmor et al., Phys. Rev. B, 59 (1999), pp. 235--245]. Another existing numerical approach to modeling multilattices is homogenization. In the present paper we review the existing numerical methods for multilattices and propose another concurrent macro-to-micro method in the numerical homogenization framework. We give a unified mathematical formulation of the new and the existing methods and show their equivalence. We then consider extensions of the proposed method to time-dependent problems and to random materials.
Read More: http://epubs.siam.org/doi/abs/10.1137/110841163
Read More: http://epubs.siam.org/doi/abs/10.1137/110841163
Original language | English |
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Pages (from-to) | 696-726 |
Number of pages | 31 |
Journal | Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal |
Volume | 10 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2012 |