An atomistic derivation of von-Kármán plate theory

Abstract

<p style='text-indent:20px;'>We derive <i>von-Kármán plate theory</i> from three dimensional, purely atomistic models with classical particle interaction. This derivation is established as a <inline-formula><tex-math id="M1">\begin{document}$ \Gamma $\end{document}</tex-math></inline-formula>-limit when considering the limit where the interatomic distance <inline-formula><tex-math id="M2">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> as well as the thickness of the plate <inline-formula><tex-math id="M3">\begin{document}$ h $\end{document}</tex-math></inline-formula> tend to zero. In particular, our analysis includes the <i>ultrathin</i> case where <inline-formula><tex-math id="M4">\begin{document}$ \varepsilon \sim h $\end{document}</tex-math></inline-formula>, leading to a new <i>von-Kármán plate theory for finitely many layers</i>.</p>