A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics

M. Dobson; R. S. Elliott; M. Luskin; E. B. Tadmor

doi:10.1007/s10820-007-9084-7

A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics

M. Dobson, R. S. Elliott, M. Luskin, E. B. Tadmor

Research output: Contribution to journal › Article › peer-review

36 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	219-237
Number of pages	19
Journal	Journal of Computer-Aided Materials Design
Volume	14
Issue number	SUPPL. 1
DOIs	https://doi.org/10.1007/s10820-007-9084-7
State	Published - Dec 2007

Bibliographical note

Funding Information:
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.

Keywords

Cascading Cauchy-Born
Finite elements
Multilattice
Multiscale
Quasicontinuum

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A multilattice quasicontinuum for phase transforming materials: Cascading Cauchy Born kinematics

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