On the Passage from Atomic to Continuum Theory for Thin Films

We give a rigorous derivation of a continuum theory from atomic models for thin films. This scheme has been proposed by Friesecke and James in J. Mech. Phys. Solids 48, 1519–1540 (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 ν-1 director fields when ν is the (fixed) number of atomic film layers.