Research Group of Prof. Dr. M. Griebel
Institute for Numerical Simulation

  author = {M.~Arndt and M.~Griebel},
  title = {Higher order gradient continuum description of atomistic
		  models for crystalline solids},
  booktitle = {Proceedings of the Fourth European Congress on
		  Computational Methods in Applied Sciences and Engineering,
		  Jyv\"askyl\"a, Finland},
  year = {2004},
  editor = {P. {Neittaanm\"aki} and others},
  ps = { 1},
  pdf = { 1},
  annote = {series,C4,multi},
  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
		  deformation 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
		  crystal. The resulting approximation properties are studied
		  in a stationary setting. Finally, a numerical simulation of
		  the time evolution of the elastic response of crystal
		  silicon is presented.}