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European Congress on Computational Methods in Applied Sciences and Engineering ECCOMAS 2004
 

Summary: European Congress on Computational Methods in Applied Sciences and Engineering
ECCOMAS 2004
P. Neittaanm¨aki, T. Rossi, S. Korotov, E. O~nate, J. P´eriaux, and D. Kn¨orzer (eds.)
Jyv¨askyl¨a, 24­28 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: {arndt,griebel}@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 effects
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-

  

Source: Arndt, Marcel - School of Mathematics, University of Minnesota
Bebendorf, Mario - Institut für Numerische Simulation, Universität Bonn

 

Collections: Computer Technologies and Information Sciences; Mathematics