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Summary: European Congress on Computational Methods in Applied Sciences and Engineering
ECCOMAS 2004
P. Neittaanmaki, T. Rossi, S. Korotov, E. O~nate, J. Periaux, and D. Knorzer (eds.)
Jyvaskyla, 24{28 July 2004
HIGHER ORDER GRADIENT CONTINUUM
DESCRIPTION OF ATOMISTIC MODELS FOR
CRYSTALLINE SOLIDS
Marcel Arndt ? , Michael Griebel ?
? Institute for Numerical Simulation, University of Bonn,
Wegelerstr. 6, 53115 Bonn, Germany
e-mail: farndt,griebelg@ins.uni-bonn.de, web page: http://www.ins.uni-bonn.de
Key words: continuum limit, quasi-continuum approximation, upscaling, molecular dy-
namics, continuum mechanics, multiscale simulation
Abstract. We propose an upscaling scheme for the passage from atomistic to continuum
mechanical models of crystalline solids. It is based on a Taylor expansion of the deforma-
tion function up to a given order and describes the material properties to a higher extent
than commonly used continuum mechanical models. In particular, the discreteness e ects
of the underlying atomistic model are captured. The qualitative properties of the technique
are numerically analyzed for the model problem of a one-dimensional atomic chain. The
approach is then applied to the real three-dimensional physical example of a silicon crys-
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