# An atomistic derivation of von-K\'arm\'an plate theory

## TL;DR

This paper rigorously derives the classical von-Kármán plate theory from atomistic models by analyzing the limit as interatomic distance and plate thickness approach zero, including ultrathin cases with finitely many layers.

## Contribution

It provides a novel derivation of von-Kármán plate theory directly from atomistic models using $ ext{Gamma}$-convergence, covering ultrathin plates with finitely many layers.

## Key findings

- Derivation of von-Kármán theory from atomistic models.
- Extension to ultrathin plates with finitely many layers.
- Establishment of the $ ext{Gamma}$-limit in the derivation.

## Abstract

We derive von-K\'arm\'an 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 $\varepsilon$ as well as the thickness of the plate $h$ tend to zero. In particular, our analysis includes the ultrathin case where $\varepsilon \sim h$, leading to a new von-K\'arm\'an plate theory for finitely many layers.