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On the passage from atomic to continuum theory for thin films. (English) Zbl 1156.74028
Summary: We give a rigorous derivation of a continuum theory from atomic models for thin films. This scheme has been proposed by G. Friesecke and R. D. James in [J. Mech. Phys. Solids 48, No. 6–7, 1519–1540 (2000; Zbl 0984.74009)]. 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.

74K35 Thin films
74A25 Molecular, statistical, and kinetic theories in solid mechanics
Full Text: DOI
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