An atomistic derivation of von-Kármán plate theory

Abstract

We derive von-Kármán plate theory from three dimensional, purely atomistic models with classical particle interaction. This derivation is established as a $\Gamma$-limit when considering the limit where the interatomic distance $\epsilon$ as well as the thickness of the plate $h$ tend to zero. In particular, our analysis includes the ultrathin case where $\epsilon \sim h$, leading to a new von-Kármán plate theory for finitely many layers.