The quasicontinuum (QC) method is applied to materials possessing a multilattice crystal structure. Cauchy-Born (CB) kinematics, which accounts for the shifts of the crystal basis, is used in continuum regions to relate atomic motions to continuum deformation gradients. To avoid failures of the CB kinematics, QC is augmented with a phonon stability analysis that detects lattice period extensions and identifies the minimum required periodic cell size. This augmented approach is referred to as Cascading Cauchy-Born kinematics. The method is analyzed for both first- and second-order phase transformations, and demonstrated numerically on a one-dimensional test problem.
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Acknowledgements This work was supported in part by the Department of Energy under Award Number DE-FG02-05ER25706, NSF grant DMS-0304326, and by the University of Minnesota Supercomputing Institute.
- Cascading Cauchy-Born
- Finite elements