A Quasicontinuum for Complex Crystals
by
M. Dobson, R. S. Elliott and E. B. Tadmor
in
Proceedings of the Third International Conference on Multiscale Materials Modeling, pp. 889–896, Sept, 2006.
Category: Conf. Proceeding
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Abstract:
The quasicontinuum (QC) method is extended to materials possessing complex crystal structures. This requires a generalization of the Cauchy-Born (CB) kinematics, which is used in the continuum region to relate atomic motions to continuum deformation gradients, to account for the shuffles of the crystal sub-lattices. In addition, in order to prevent failures of the CB kinematics, it is augmented with a phonon stability analysis that detects lattice period extensions and identifies the minimum required cell size. This augmented approach is referred to as cascading Cauchy-Born kinematics. To prevent the formation of degenerate symmetry-related structures and to introduce a physical lengthscale into the continuum, an estimate for the interfacial energy is added to the total energy. The method is demonstrated for a number of one-dimensional test problems.
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