A Derivation of Continuum Nonlinear Plate Theory from Atomistic Models

We derive plate theory from atomistic models in the spirit of [G. Friesecke, R. D. James, and S. Müller, Comm. Pure Appl. Math., 55 (2002), pp. 1461–1506] as a Γ‐limit as the number of atoms tends to infinity. While in the “thick film regime,” i.e., when the film consists of many layers of atoms, we recover the well‐known plate theory derived from three‐dimensional elasticity in [G. Friesecke, R. D. James, and S. Müller, Comm. Pure Appl. Math., 55 (2002), pp. 1461–1506]; for “thin films” new terms in the limit functional are obtained. These terms are due to the discrete nature of atomic models and surface effects and cannot be detected from continuum elasticity.