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COMPUTATIONAL MECHANICS WCCM VI in conjunction with APCOM'04, Sept. 5-10, Beijing, China

WCCM VI in conjunction with APCOM'04, Sept. 5-10, Beijing, China
c 2004 Tsinghua University Press & Springer-Verlag
Upscaling Technique for the Atomistic-Continuum Simulation of
Shape Memory Alloys with the EAM Potential
Marcel Arndt1
1Institute for Numerical Simulation, University of Bonn, Wegelerstr. 6, 53115 Bonn, Germany
e-mail: arndt@ins.uni-bonn.de, www: http://www.ins.uni-bonn.de
Abstract. In this paper the upscaling process for the passage from atomistic to continuum mechanical models
of shape memory alloys is considered. First the modeling on the atomistic level is reviewed and a numerical
simulation of a Ni64Al36 alloy is presented. Then the upscaling to an intermediate continuum mechanical
model is performed by means of the inner expansion technique. This model is further approximated to
extract the essential properties. The resulting continuum mechanical model is finally used for the numerical
simulation of a SMA-based two-way micro-actuator.
Key words. Upscaling, multiscale simulation, continuum limit, quasi-continuum approximation, shape
memory alloy.
1 Introduction
Many materials exhibit a complex behavior which needs to be resolved on different length scales. Macro-
scopic effects can often be well described by models on the continuum mechanical level, whereas for micro-
scopical effects the atomistic level with the method of Molecular Dynamics (MD) is appropriate. Sometimes


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


Collections: Computer Technologies and Information Sciences; Mathematics