@Article{	  Arndt.Griebel:2005,
  author	= {Marcel Arndt and Michael Griebel},
  title		= {Derivation of higher order gradient continuum models from
		  atomistic models for crystalline solids},
  journal	= {Multiscale Modeling and Simulation},
  volume	= {4},
  number	= {2},
  pages		= {531-562},
  note		= {Also as Preprint No.~152, SFB 611, University of Bonn},
  year		= {2005},
  pdf		= {http://wissrech.ins.uni-bonn.de/research/pub/arndt/60873.pdf}
		  ,
  abstract	= {We propose a new upscaling scheme for the passage from
		  atomistic to continuum mechanical models for crystalline
		  solids. It is based on a Taylor expansion of the
		  deformation function and allows to capture the microscopic
		  properties and the discreteness effects of the underlying
		  atomistic system up to an arbitrary order. The resulting
		  continuum mechanical model involves higher order terms and
		  gives a description of the specimen within the
		  quasi-continuum regime. Furthermore the convexity of the
		  atomistic potential is retained, which leads to well-posed
		  evolution equations. We numerically compare our technique
		  to other common upscaling schemes for the example of an
		  atomic chain. Then we apply our approach to a physically
		  more realistic many-body potential of crystalline silicon.
		  Here, the above mentioned advantages of our technique hold
		  for the newly obtained macroscopic model as well.},
  annote	= {article,sfb611preprint,C4,multi}
}