Numerical methods for multilattices

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.


Published in:
SIAM, Multiscale Modeleling Simulation, 10, 3, 696-726
Year:
2012
Publisher:
Philadelphia, Siam Publications
Keywords:
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 Record created 2012-11-07, last modified 2018-03-17

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