On the passage from atomic to continuum theory for thin films

Bernd Schmidt

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Submission date: 13. Sep. 2005
Pages: 54
published in: Archive for rational mechanics and analysis, 190 (2008) 1, p. 1-55 
DOI number (of the published article): 10.1007/s00205-008-0138-0
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Abstract:
We give a rigorous derivation of continuum theory from atomic models for thin films as proposed by Friesecke and James in [JMPS 48 (2000)]. The resulting continuum energy expression is obtained by integrating a stored energy density which not only depends on the deformation gradient but also on director fields when is the (fixed) number of atomic film layers.