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arXiv · 1907.00197

An atomistic derivation of von-Kármán plate theory

Julian Braun·Bernd Schmidt
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Abstract

We derive von-Kármán plate theory from three dimensional, purely atomistic models with classical particle interaction. This derivation is established as a $Γ$-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-Kármán plate theory for finitely many layers.

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Julian Braun, Bernd Schmidt. 2019-06-29. An atomistic derivation of von-Kármán plate theory. https://arxiv.org/abs/1907.00197

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