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On the passage from atomic to continuum theory for thin films
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 $\nu-1$ director fields when $\nu$ is the (fixed) number of atomic film layers.